Linear Algebra (Spring 2018) by James Cook at Liberty University

source: James Cook      2018年1月22日
I intent to post my lectures from the Spring 2018 offering of Math 321 at Liberty University. I'll also post the help session which I run most Thursdays. This course has a prerequisite of a proof course, so, it is at a higher level than some linear algebra courses which are intended for a less advanced audience. The basic plan is to cover matrices and equations in Part I, then vectors spaces and basic theory in Part II then in the last third of the course we study Jordan form and the real spectral theorem as well as a few applications.

1 45:36 rings and things, matrices and components, 1-22-18
2 52:42 standard bases and matrix multiplication, 1-24-18
3 59:51 help session on matrix multiplication and index calculation, 1-25-18, part 1
4 12:57 help session on matrix multiplication and index calculation, 1-25-18, part 2
5 41:18 further matrix multiplication, 1-26-18
6 53:11 properties of inverse, types of matrices, 1-29-18
7 51:42 blocks, row operations introduced, 1-31-18
8 59:51 help session on row reduction, 2-1-18, part 1
9 17:22 help session on row reduction, 2-1-18, part 2
10 51:44 from row reduction to elementary matrices, 2-2-18
11 50:55 equivalent conditions for invertibility, 2-5-18
12 59:51 help session on CCP, LI and span, 2-8-18, part 1
13 18:08 help session on CCP, LI and span, 2-8-18, part 2
14 53:46 proof of CCP, super-augmented matrix, 2-9-18
15 49:30 determinants motivated, formulas, expansion by minors, 2-12-18
16 52:34 inverse criteria, Cramer's Rule, inverse formula, 2-14-18
17 59:51 help session, wedges, determinant, evectors, fun, 2-15-18 part 1
18 8:52 help session, wedges, determinant, evectors, fun, 2-15-18 part 2
19 43:00 review for Test 1, 2-16-18
20 50:34 vector spaces and subspaces, 2-21-18
21 59:51 help session, post-mortem of Test 1, subspace examples, 2-22-18, part 1
22 5:11 help session, post-mortem of Test 1, subspace examples, 2-22-18, part 2
23 50:01 span and LI in vector space, 2-23-18
24 49:11 basis and coordinates introduced, 2-26-18
25 52:11 on coordinate calculation, constructive proof of dim, 2-28-18
26 59:51 help session on coordinates and basis calculation, 3-1-18, part 1
27 12:21 help session on coordinates and basis calculation, 3-1-18, part 2
28 49:07 dimension theorems, linear transformation, 3-2-18
29 52:06 linear transformations leading to isomorphism, 3-5-18
30 6:25 examples of transformations on plane etc. 3-7-18, part 1
31 11:11 FToLA and the standard matrix, 3-7-18, part 2
32 9:56 restriction and linear extension, 3-7-18, part 3
33 21:16 matrix of abstract linear map, 3-7-18, part 4
34 59:51 help session on inverse image idea, 3-8-18, part 1
35 9:01 help session on matrix of linear map etc, 3-8-18, part 2
36 53:18 help for the weary, 3-9-18
37 6:22 coordinate change vectors, 3-12-18, part 1
38 7:02 coordinate change vectors, 3-12-18, part 2
39 6:22 coordinate change vectors, 3-12-18, part 3
40 11:19 coordinate change matrices, 3-12-18, part 4
41 11:56 coordinate change matrices, 3-12-18, part 5
42 3:47 rank nullity theorem, linear algebraic proof, 3-12-18, part 6

[lectures in English] 線性代數 Linear Algebra--林源倍 / 交大

source: NCTU OCW     2017年12月28日
YouTube Playlist: https://www.youtube.com/playlist?list...
課程資訊: http://ocw.nctu.edu.tw/course_detail....
更多課程歡迎瀏覽交大開放式課程網站：http://ocw.nctu.edu.tw/
本課程是由交通大學電機工程學系提供。 (This course is taught in English.)

1 10:18 CH1.1 Matrices and Vectors
2 13:59 CH1.2 Linear Combination, matrix-vector product, and special matrices
3 15:48 CH1.3-1 System of linear equation PartI
4 19:13 CH1.3-2 System of linear equation PartII
5 14:07 CH1.4-1 Gaussion elimination Part I
6 17:17 CH1.4-2 Gaussion elimination Part II
7 21:03 CH1.6-1 Span Part I
8 11:14 CH1.6-2 Span Part II
9 19:52 CH1.7-1 Linearly independent sets and Linearly dependent sets Part I
10 16:54 CH1.7-2 Linearly independent sets and Linearly dependent sets Part II
11 14:51 Ch2 Matrices and linear transformation CH2.1 matrix multiplication
12 24:14 CH2.3 Invertible matrices and Elementary matrices
13 11:25 CH2.3 Invertible matrices and Elementary matrices CH2.4 Inverses Part I
14 20:06 CH2.3 Invertible matrices and Elementary matrices CH2.4 Inverses Part II
15 20:37 CH2.7-1 Linearly transformation and matrices Part I
16 5:41 CH2.7-2 Linearly transformation and matrices Part II
17 9:07 CH2.8-1 Composition and invertibility of linear tr Part I
18 9:54 CH2.8-2 Composition and invertibility of linear tr Part II
19 10:55 CH3 Determinants CH3.1Cofactor expansion
20 21:33 CH3.2-1 Properties of determinants Part I
21 10:44 CH3.2-2 Properties of determinants Part II
22 10:19 CH4 Subspaces and Properties
23 5:16 CH4.2-1 Basis and dimension Part I
24 11:29 CH4.2-2 Basis and dimension Part II
25 7:29 CH4.2-3 Basis and dimension Part III
26 13:48 CH4.3 Dimension of ColA, RowA, NullA
27 12:01 CH4.4-1 Coordinate systems Part I
28 13:51 CH4.4-2 Coordinate systems Part II
29 10:48 CH4.5 Matrix representationof linear operator
30 14:00 CH5 Eigen values, eigen vectors and diagonalization
31 10:18 CH5.2-1 Characteristic Polynomials Part I
32 17:41 CH5.2-2 Characteristic Polynomials Part II
33 34:42 CH5.3 Diagonalization of matrices
34 12:34 CH6 Orthogonality CH6.1-1 Geometry of vectors Part I
35 8:39 CH6.1-2 Geometry of vectors Part II
36 12:45 CH6.2-1 Orthogonal Vectors (orch) Part I
37 30:33 CH6.2-2 Orthogonal Vectors (orch) Part II
38 22:00 CH6.3-1 Orth. Projection Part I
39 25:18 CH6.3-2 Orth. Projection Part II
40 15:18 CH6.4-1 Least-squares approximation and o.p. matrices Part I
41 12:50 CH6.4-2 Least-squares approximation and o.p. matrices Part II
42 11:01 CH6.5 Orth. matrices
43 23:27 CH6.6-1 Symmetric matrices Part I
44 24:43 CH6.6-2 Symmetric matrices Part II
45 18:35 CH6.7-1 Singular value decomposition Part I
46 15:12 CH6.7-2 Singular value decomposition Part II
47 27:04 CH7 Vector spaces CH 7.1-1 Vector spaces and their subspace Part I
48 10:07 CH 7.1-2 Vector spaces and their subspace Part II
49 24:30 CH 7.2-1 Linear transformations Part I
50 24:33 CH 7.2-2 Linear transformations Part II
51 23:32 CH 7.3-1 Basis and Dimensions Part I
52 5:50 CH 7.3-2 Basis and Dimensions Part II
53 15:04 CH 7.4-1 Matrix representation of linear operator Part I
54 10:15 CH 7.4-2 Matrix representation of linear operator Part II
55 13:43 CH 7.5-1 Inner product space Part I
56 14:27 CH 7.5-2 Inner product space Part II

Applied Linear (Spring 2017) by James Cook

# You can also click the upper-left icon to select videos from the playlist.

source: James Cook      2017年1月18日
Here are my Lectures from Math 221, a Sophomore level linear algebra course which is intended for engineering or other applied technical majors. We're using Thomas Shores' Applied Linear Algebra text, but, I'm likely to supplement with some of my own materials from past teaching of linear algebra.

systems of equations, Gauss Jordan, 1-17-17, part 1 59:51 Note, the excellent webtool I use in this Lecture is found at: http://www.math.odu.edu/~bogacki/cgi-...
systems of equations, Gauss Jordan, 1-17-17, part 2 7:44
complex arithmetic, how to factor polynomials over C, 1-19-17, part 1 59:51
complex arithmetic, how to factor polynomials over C, 1-19-17, part 2 16:43
complex example, structure of solution sets, 1-24-17, part 1 59:51
complex example, structure of solution sets, 1-24-17, part 2 15:31
matrix algebra and multiplication, 1-26-17, part 1 59:51
matrix algebra and multiplication, 1-26-17, part 2 17:49
on interpretations of the rref of a given matrix, finding inverses, 1-31-17 54:39
matrix column multiplication, blocks, 2-2-17, part 1 59:51
matrix column multiplication, blocks, 2-2-17, part 2 9:21
rank, linear transformation and its standard matrix, 2-7-17, part 1 59:51
rank, linear transformation and its standard matrix, 2-7-17, part 2 16:25
partial derivatives and linearization, determinants, 2-14-17, part 1 59:51
partial derivatives and linearization, determinants, 2-14-17, part 2 15:32
Cramer's Rule, Vector Space and Subspace, 2-16-17, part 1 59:51
Cramer's Rule, Vector Space and Subspace, 2-16-17, part 2 14:53
help with Mission 1, span, LI and coordinates, 2-21-17, part 1 59:51
help with Mission 1, span, LI and coordinates, 2-21-17, part 2 17:37
bases for matrix subspaces, words on Test 1, 2-23-17, part 1 59:33
bases for matrix subspaces, words on Test 1, 2-23-17, part 2 14:13
Test 1 overview, coordinate change and linear maps, 3-2-17, part 1 59:51
Test 1 overview, coordinate change and linear maps, 3-2-17, part 2 16:08
orthonormality in Euclidean space, 3-7-17, part 1 59:51
orthonormality in Euclidean space, 3-7-17, part 2 21:41
normal equation, linear least squares, 3-9-17, part 1 59:51
normal equation, linear least squares, 3-9-17, part 2 16:11
some hwk advice, inner product space, 3-21-17, part 1 59:51
some hwk advice, inner product space, 3-21-17, part 2 2:26
complex inner product space, orthogonal things, 3-23-17, part 1 59:51
complex inner product space, orthogonal things, 3-23-17, part 2 15:57
unitary matrices, help on homework, 3-28-17, part 1 59:51
unitary matrices, help on homework, 3-28-17, part 2 25:16
eigenvectors and values, spectral theorem, 4-6-17, part 1 59:51
eigenvectors and values, spectral theorem, 4-6-17, part 2 15:28
diagonalization and applications, 4-11-17, part 1 59:51
diagonalization and applications, 4-11-17, part 2 13:18
quadratic forms and eigenvectors, 4-13-17, part 1 59:51
quadratic forms and eigenvectors, 4-13-17, part 2 2:58
complex eigvectors, jordan blocks, deqns, 4-18-17, part 1 59:51
complex eigvectors, jordan blocks, deqns, 4-18-17, part 2 16:12
review of Test 3 solution, reminders about Tests 1,2, 5-2-17, part 1 59:51
comments about final, 5-2-17, part 2 8:56

Linear Algebra (Spring 2015) by James Cook

# You can also click the upper-left icon to select videos from the playlist.

source: James Cook      2015年1月14日
These videos are from Math 321 at Liberty University from the Spring 2015 Semester. I followed my notes which are found at: http://www.supermath.info/LinearNotes2015.pdf and in 2015 we used "A Course in Linear Algebra" (a Dover publication) by David B. Damiano and John B. Little. In 2014 I used the open source Linear Algebra text by Jim Hefferon and in 2016 I'm using "Linear Algebra: An Introductory Approach" by Charles W. Curtis (from Springer). Of course, there are probably hundreds of excellent linear algebra texts, these choices are a mixture of economy and fit to the prerequisite structure at our school. For example. I do assume you have previous experience with mathematical proof. However, very little background is really needed. I would recommend watching the 2016 course as it is posted. I bought a mic and the audio is vastly improved.

Lecture 1 part 1: sets, index notation, rows and columns 33:26 Introductory comments about numbers, sets, notation. Based on Chapter 1 of http://www.supermath.info/LinearNotes...
Lecture 1 part 2: equality by components, rows or columns 7:18
Lecture 2 part 1: functions, Gaussian elimination 33:26
Lecture 2 part 2: row reduction for solving linear systems 11:36
Lecture 3: solution sets, some theoretical results about rref 49:01
Lecture 4: rref pattern, fit polynomials, matrix algebra basics 50:02
Lecture 5: prop of matrix algebra, all bases belong to us, inverse matrix defined 52:02
Lecture 6: elementary matrices, properties and calculation of inv. matrix 49:29
Lecture 7 50:04
Lecture 8 51:31
Lecture 9: LI and the CCP 39:19
Lecture 9 bonus 15:45
Lecture 11: gallery of LT, injectivity and surjectivity for LT, new LT from old 51:54
Lecture 12: examples and applications of matrices and LTs 48:42
Lecture 13 part 1 32:27
Lecture 13 part 2: solution to Quiz 1 22:06
Lecture 14: vector space defined, examples, subspace theorem 49:37
Lecture 15: axiomatic proofs, subspace thm proof, Null(A) and Col(A) 49:02
Lecture 16: generating sets for spans, LI, basis and coordinates 50:16
proofs before Lecture 17 0:28
Lecture 17: theory of dimension and theorems on LI and spanning 54:01
Lecture 18: basis of column and null space, solution set structure again 50:01
Lecture 19: subspace thms for LT and unique linear extension prop 53:29
Lecture 19.5: isomorphism is equivalence relation, finite dimension classifies 25:02
Lecture 20 part 1: coordinate maps and matrix of LT for abstract vspace 31:34
Lecture 20 part 2: examples of matrix of LT in abstract case 22:34
Lecture 21: kernel vs nullspace, coordinate change 51:11
Lecture 22 part 1: coordinate change for matrix of LT 46:35
Lecture 22 part 2:rank nullity, Identity padded zeros thm, matrix congruence comment 5:07
Lecture 22.5: proof of abstract rank nullity theorem, examples 26:43
Lecture 23: part 1: quotient of vector space by subspace 30:19
Lecture 23 part 2: quotient space examples,1st isomorphism theorem 35:29
Lecture 24: structure of subspaces, TFAE thm for direct sums 51:56
Review for Test 2 part 1 59:51
Review for Test 2 part 2 35:39
Lecture 26: motivation, calculation and interpretation of determinants 48:24
Lecture 27: determinant properties, Cramer's Rule derived 48:54
Lecture 28: adjoint formula for inverse, eigenvectors and values 52:45
interesting example for Lecture 28 2:59
Lecture 28 additional eigenvector examples 16:02
Lecture 29: basic structural theorems about eigenvectors 51:59
supplement to Lecture 29 11:25
Lecture 30: eigenspace decompositions, orthonormality 52:24
concerning rotations 21:47
Lecture 31: complex vector spaces and complexification 52:26
Lecture 32: rotation dilation from complex evalue, GS example 53:01
Lecture 33: orthonormal bases, projections, closest vector problem. 53:30
Lecture 34: complex inner product space, Hermitian conjugate and properties 52:51
Problem 154 solution 0:45
Lecture 35: overview of real Jordan form, application to DEqns 52:16
Lecture 36: invariant subspaces, triangular forms, nilpotentence 52:59
Lecture 37: nilpotent proofs, diagrammatics for generalize evectors, A = D + N 49:11
Lecture 38: minimal polynomial, help with homework 52:47
Lecture 39: quiz 3 solution 49:43
partial course review 1:16:15

Linear Algebra (Spring 2016) by James Cook

# You can also click the upper-left icon to select videos from the playlist.

source: James Cook      2016年1月18日
I intend to post the Lectures from Math 321 of Spring 2016. See: http://www.supermath.info/math321PlannerSpring2016.pdf for the plan. We're using Charles W. Curtis’ Linear Algebra An Introductory
Approach as the required text. However, the first few lectures on matrix calculation are not in sync with the required text. I hope to post Lecture Notes to follow this plan as the semester continues.

Jan 18, introduction, some algebraic language 51:06
Jan 20, finite sums and matrix ops defined 51:09
Jan 22, some proofs of matrix algebra part 1 31:57
Jan 22, concatenation proof help, part 2 5:47
Jan 22, all the bases belong to us, part 3 7:29
Jan 22, inverses, 2x2 formula, part 4 18:28
Jan 22, symmetric, triangular, diagonal, nilpotent, part 5 12:42
Jan 25, systems of equations, Gauss-Jordan Algorithm 52:39
supplement 1 for Jan 25, a row reduction over Z/11Z 9:42
Jan 27, elementary matrices, theorem(s) of invertibility 51:47
Jan 29, end of inverses, span and LI, CCP 52:30
Feb 1, review of course up to this point 49:27
Feb 5, Vector Space, subspace tests 53:59
Feb 8, span theorem, linear independence (LI), basis defined 49:13
Feb 12, structure of solution sets 50:44
Feb 15, snow day, bonus basis examples, subspace theorem sketch 35:02
Feb 17, basic theory of linear transformations 51:38
Feb 19, linear transformations part 1 51:31
Feb 19, linear transformations part 2 59:51
Feb 19, linear transformations part 3 8:13
Feb 22, matrix of transformation again 52:49
Feb 24, coordinate change for vectors and transformations 54:08
Feb 26, day of the determinant 51:49
Feb 29, comments for Test 1 44:20
March 4, inverse formula, classification problem for L(V) 51:39
March 9, 2016, divisibility of minimal polynomial, e-vectors defined 51:17
March 11, e-vectors, invariant subspaces, diagonalizable, examples 52:26
E.M.L. 1, invariant subspaces, primary decomposition theorem 23:19
E.M.L. 2, idempotent examples the E_i and q_i and the a_i of the proof 22:35
E.M.L. 3, diagonalizable transformations, simultaneous diagonalization 15:25
E.M.L. 4, triangular form theorem, nilpotence 26:30
E.M.L. 5, minimal vs characteristic poly examples, Jordan Decomposition Theorem 22:26
E.M.L. 6, elementary divisor theorem, companion matrices, rational canonical form 43:28
March 21, rational and Jordan forms, chains of generalized e-vectors 49:31
March 23, rational vs Jordan form an attempt, complexification 49:36
March 25, real Jordan form 53:29
March 30, differential equations via the matrix exponential 52:40
April 1, real inner product space 51:48
April 4, orthonormality and Gram Schmidt Algorithm 52:52
April 8, theory of orthogonal complements, least squares 52:15
April 11, orthogonal transformations, real spectral theorem, quadratic forms 52:24
April 13, word on complex inner products, quotient space 53:55
April 15, first isomorphism theorem, dual space 52:40
April 18, hwk help, double dual, bilinear forms (part 1) 52:35
April 20, metric vs. inner product, geometries, musical morphisms 50:51
April 22, tensor products over and on a vector space 52:38
Solution to Mission 9, a video overview 11:12
April 25, review for Test 2 46:42
SubscribeOrIBiteYourHeadOff 3:22
May 2, a word on Hurwitz Theorem, Daniel Attacks. 46:53

Linear Algebra (Spring 2017) by James Cook at Liberty University

# You can also click the upper-left icon to select videos from the playlist.

source: James Cook           2017年1月16日
This playlist contains my Lectures from Math 321 in the Spring 2017 Semester at Liberty University. This Semester I do not follow a particular text. Instead, we just use my notes (which are based on about 10 popular texts in linear algebra).
The level of this course is higher than some courses which do not have a proof course prerequisite. Unfortunately, many of the common texts are really written more as a cookbook of problem solving techniques. The flavor here is decidedly less applied. This is a math course and while we mention applications, the centerpiece is simply the theoretical structure of linear algebra. The theory here is both simple and general. For the student of math, linear algebra is a great place to hone proof writing skill. We wish this course to increase the skill of the student in formal argument and abstraction. Naturally, we also seek for students of this course to assimilate the central theorems and intuitions of linear algebra. Fortunately, the goal of learning linear algebra well fits naturally with the goal of embracing abstraction in mathematics. If you want an applied linear algebra course where the focus is not on proofs then you ought to take our Math 221 course if you are a student at Liberty. We will also cover applications, but, our emphasis is not on problem solving.

components, rows, columns, add and scalar multiply, word on rings: 1-16-17 46:51
standard notations, matrix multplication, 1-20-17 52:40
how to multiply with standard bases, special matrices, 1-20-17 56:56
supplemental examples of block multiplication, for 1-20-17 4:59
on the Gauss-Jordan algorithm, 1-23-17 53:22
on the structure of solution sets and elementary matrices, 1-25-17 51:23
on inverse matrices, 1-27-17 53:15
spanning, linear independence and CCP for column vectors, 1-30-17 51:52
CCP proof and its application, motivation of determinants, 2-1-17 52:04
on determinant calculation, 2-3-17 48:33
Cramer's Rule and the Adjoint Formula for the Inverse, 2-6-17 51:17
definition of vector space, examples, subspace test, 2-13-17 51:28
subspace examples, span, basis, 2-15-17, part 1 59:51
subspace examples, span, basis, 2-15-17, part 2 6:11
on coordinates and dimension, 2-17-17 51:09
theorems on manipulating bases, 2-20-17 53:30
the subspace theorem (in my office), 2-20-17 26:52
basic theory of linear transformations, 2-22-17 51:39
theorem on image and inverse image, standard matrx, 2-24-17 47:28
gallery of linear transformations, restriction, matrix of T, 2-27-17 54:31
finite dimensional isomorphism, matrix of linear transformation, 3-1-17 51:26
matrix of linear maps, coordinate change, 3-3-17 54:18
rank nullity for maps, congruence vs. similarity, 3-6-7 51:44
direct sum decomposition part 1, 3-8-17 51:50
direction sum decomposition theorem part 2, 3-10-17 8:50
direct sum of matrices, intro eigenvectors, 3-10-17 50:27
eigenbasis, algebraic and geometric multiplicity, 3-20-17 51:20
Jordan Form for Matrix or Transformation, 3-22-17 51:11
review for Test 2, 3-24-17 51:35
technology assessment, 3-29-17 29:41
Easter Monday video on polynomial op theory, 3-31-17 44:42
examples of Jordan forms, Matrix Exponential, 4-3-17 50:25
differential equations, inner products, 4-5-17 54:31
orthogonal, GSA example, 4-7-17 55:27
orthogonal complements, 4-10-17 47:54
angles in complex inner product space, least squares, adjoint, 4-12-17 53:19
explicit formula for adjoint, linear isometries, dual space, 4-14-17 52:59
partial proof of spectral theorems, 4-19-17 46:28
concluding thoughts on quadratic forms, Quotient Space intro., 4-21-17 50:37
quotient vector space and the first isomorphism theorem, 4-24-17 50:38
maps on invariant subspaces and their quotients, 4-26-17 54:02
bilinear forms, metrics, geometry, music, 4-28-17 54:10
comments about Test 3 solution and final, 5-1-17 51:46

Linear Algebra (Spring 2005) by Gilbert Strang at MIT

# click the upper-left icon to select videos from the playlist 

source: MIT OpenCourseWare     2009年5月6日
MIT 18.06 Linear Algebra, Spring 2005
Instructor: Prof. Gilbert Strang
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. *Please note that lecture 4 is unavailable in a higher quality format.
Find more lecture notes, study materials, and more courses at http://ocw.mit.edu.
View the complete course at: http://ocw.mit.edu/18-06S05
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms

Lec 1 39:49 The Geometry of Linear Equations.
Lec 2 47:42 Elimination with Matrices.
Lec 3 46:49 Multiplication and Inverse Matrices.
Lec 4 Factorization into A = LU 48:05
Lec 5 47:42 Transposes, Permutations, Spaces R^n.
Lec 6 46:01 Column Space and Nullspace.
Lec 7 43:20 Solving Ax = 0: Pivot Variables, Special Solutions.
Lec 8 47:20 Solving Ax = b: Row Reduced Form R.
Lec 9 50:14 Independence, Basis, and Dimension.
Lec 10 49:20 The Four Fundamental Subspaces.
Lec 11 45:56 Matrix Spaces; Rank 1; Small World Graphs.
Lec 12 47:57 Graphs, Networks, Incidence Matrices.
Lec 13 47:40 Quiz 1 Review.
Lec 14 49:48 Orthogonal Vectors and Subspaces.
Lec 15 48:51 Projections onto Subspaces.
Lec 16 48:05 Projection Matrices and Least Squares
Lec 17 49:25 Orthogonal Matrices and Gram-Schmidt.
Lec 18 49:12 Properties of Determinants.
Lec 19 53:17 Determinant Formulas and Cofactors.
Lec 20 51:01 Cramer's Rule, Inverse Matrix, and Volume.
Lec 21 51:23 Eigenvalues and Eigenvectors.
Lec 22 51:51 Diagonalization and Powers of A.
Lec 23 51:03 Differential Equations and exp(At).
Lec 24 51:12 Markov Matrices; Fourier Series.*
Lec 24b 48:20 Quiz 2 Review. * NOTE: the audio is in the right channel only. If you hear no audio, you are listening only to the left channel.
Lec 25 43:52 Symmetric Matrices and Positive Definiteness. * NOTE: the audio is in the right channel only. If you hear no audio, you are listening only to the left channel.
Lec 26 47:52 Complex Matrices; Fast Fourier Transform.
Lec 27 50:40 Positive Definite Matrices and Minima.
Lec 28 45:56 Similar Matrices and Jordan Form.
Lec 29 41:35 Singular Value Decomposition.
Lec 30 49:27 Linear Transformations and Their Matrices.
Lec 31 50:14 Change of Basis; Image Compression.
Lec 32 47:06 Quiz 3 Review.
Lec 33 41:53 Left and Right Inverses; Pseudoinverse.
Lec 34 43:26 Final Course Review.

Wild Linear Algebra B 27- (2014) by N J Wildberger

# click the upper-left icon to select videos from the playlist

source: njwildberger     2014年3月17日
This is the first video of Part II of this course on linear algebra, and we give a brief overview of the applications which we will be concentrating on.
The first topic will be the connections between linear algebra and Euclidean and other geometries. Linear algebra provides an excellent framework for geometry, allowing Euclid's axiomatic approach to be replaced by logically more solid definitions and proofs. However for this to work seamlessly, a more algebraic approach than found in most texts will be here adopted. We will use ideas from Rational Trigonometry, and the dot product (or inner product) will play a central role.
We motivate these developments by going back to Euclid's understanding of mathematic's most important theorem: Pythagoras' theorem, and the intimate connection with the notion of perpendicularity.

27: Geometry with linear algebra 28:12
1: Introduction to Linear Algebra (N J Wildberger) 43:31
2: Geometry with vectors 44:15
3: Center of mass and barycentric coordinates 48:11
4: Area and volume 56:03
6: Applications of 2x2 matrices 43:47
5: Change of coordinates and determinants 48:36
7: More applications of 2x2 matrices 55:13
8: Inverting 3x3 matrices 45:44
9: Three dimensional affine geometry 43:02
10: Equations of lines and planes in 3D 1:08:52
11: Applications of 3x3 matrices 53:36
12: Generalized dilations and eigenvalues 55:35
13: Solving a system of linear equations 49:13
14: More row reduction with parameters 49:13
15: Applications of row reduction (Gaussian elimination) I 41:38
16: Applications of row reduction II 57:14
17: Rank and Nullity of a Linear Transformation 1:01:09
18: The geometry of a system of linear equations 1:08:59
19: Linear algebra with polynomials 46:14
20: Bases of polynomial spaces 59:50
21: More bases of polynomial spaces 45:52
22: Polynomials and sequence spaces 1:00:49
23: Stirling numbers and Pascal triangles 58:45
24: Cubic splines (Bezier curves) using linear algebra 32:35
25: Cubic splines using calculus 41:42
26: Change of basis and Taylor coefficient vectors 50:31
28: Dot products, Pythagoras' theorem, and generalizations 27:51
29: Applications of the dot product to planar geometry I 36:06
30: Applications of the dot product to planar geometry II 45:48
31: Circles and spheres via dot products I 41:58
32: Circles and spheres via dot products II 28:14
33: The relativistic dot product 35:46
34: Oriented circles and 3D relativistic geometry I 46:12
35: Oriented circles and relativistic geometry II 50:39
36: Energy, momentum and linear algebra 46:03
37: An elementary introduction to Special Relativity I 46:40
38: An elementary introduction to Special Relativity II 55:48
39: Length contraction, time dilation and velocity addition 1:00:40
40a: Relativistic dot products and complex numbers 38:06
40b: Relativistic dot products and complex numbers II 25:28
41: The chromatic algebra of 2x2 matrices I 32:14
42: The chromatic algebra of 2x2 matrices II 37:56

Wild Linear Algebra A 1-26 (2011) by Norman J Wildberger at UNSW

# click the upper-left icon to select videos from the playlist 

source: njwildberger    2011年3月7日
A course on Linear Algebra. Given by N J Wildberger of the School of Mathematics and Statistics at UNSW, the course gives a more geometric and natural approach to this important subject, with lots of interesting applications. Our orientation is that Linear Algebra is really ``Linear Algebraic Geometry'': so teaching the algebra without the geometry is depriving the student of the heart of the subject.
Intended audience: first year college or undergraduate students, motivated high school students, high school teachers, general public interested in mathematics. Enjoy!
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .

1: Introduction to Linear Algebra (N J Wildberger) 43:31 The first lecture discusses the affine grid plane and introduces vectors, along with the number one problem of linear algebra: how to invert a linear change of coordinates!
CONTENT SUMMARY: pg 1: @00:10 N. J. Wildberger Webpages:
web.maths.unsw.edu.au/~norman/­index.html
pg 2: @02:10 Linear Algebra to Linear Algebraic Geometry; example; applications
pg 3: @04:52 2-dim affine geometry (no notion of perpendicularity); affine grid plane; the core problem of linear algebra
pg 4: @09:27 no distance measurement, no special point (origin), no angle
measurement; relative positions can be described; affine grid plane; vector;
connection between algebra and geometry
pg 5: @13:52 refinement of the affine grid plane; rational number
pg 6: @17:34 Multiples of a vector; adding vectors; basis vectors e1 and e2
pg 7: @22:34 Two affine grids and 2 sets of basis vectors
pg 8: @27:13 change of basis vectors example
pg 9: @30:47 change of basis example continued; Main Problem of Linear Algebra (MPLA)
pg 10: @34:03 summary of previous example; (MPLA) General case in 1dim; (MPLA) General case in 2dim
pg 11: @40:32 questions; Exercise 1.1
pg 12: @41:42 Exercises 1.2-4. (THANKS to EmptySpaceEnterprise)
2: Geometry with vectors 44:15
3: Center of mass and barycentric coordinates 48:11
4: Area and volume 56:03
6: Applications of 2x2 matrices 43:47
5: Change of coordinates and determinants 48:36
7: More applications of 2x2 matrices 55:13
8: Inverting 3x3 matrices 45:44
9: Three dimensional affine geometry 43:02
10: Equations of lines and planes in 3D 1:08:52
11: Applications of 3x3 matrices 53:36
12: Generalized dilations and eigenvalues 55:35
13: Solving a system of linear equations 49:13
14: More row reduction with parameters 49:13
15: Applications of row reduction (Gaussian elimination) I 41:38
16: Applications of row reduction II 57:14
17: Rank and Nullity of a Linear Transformation 1:01:09
18: The geometry of a system of linear equations 1:08:59
19: Linear algebra with polynomials 46:14
20: Bases of polynomial spaces 59:50
21: More bases of polynomial spaces 45:52
22: Polynomials and sequence spaces 1:00:49
23: Stirling numbers and Pascal triangles 58:45
24: Cubic splines (Bezier curves) using linear algebra 32:35
25: Cubic splines using calculus 41:42
26: Change of basis and Taylor coefficient vectors 50:31

Linear Algebra by Norman J. Wildberger at UNSW

# click the upper-left icon to select videos from the playlist

source: njwildberger    2011年3月7日
This is the full first lecture of a course on Linear Algebra. Given by N J Wildberger of the School of Mathematics and Statistics at UNSW, the course gives a more geometric and natural approach to this important subject, with lots of interesting applications. Our orientation is that Linear Algebra is really ``Linear Algebraic Geometry'': so teaching the algebra without the geometry is depriving the student of the heart of the subject.
The first lecture discusses the affine grid plane and introduces vectors, along with the number one problem of linear algebra: how to invert a linear change of coordinates!
Intended audience: first year college or undergraduate students, motivated high school students, high school teachers, general public interested in mathematics. Enjoy!

CONTENT SUMMARY: pg 1: @00:10 N. J. Wildberger Webpages:
web.maths.unsw.edu.au/~norman/­index.html
pg 2: @02:10 Linear Algebra to Linear Algebraic Geometry; example; applications
pg 3: @04:52 2-dim affine geometry (no notion of perpendicularity); affine grid plane; the core problem of linear algebra
pg 4: @09:27 no distance measurement, no special point (origin), no angle
measurement; relative positions can be described; affine grid plane; vector;
connection between algebra and geometry
pg 5: @13:52 refinement of the affine grid plane; rational number
pg 6: @17:34 Multiples of a vector; adding vectors; basis vectors e1 and e2
pg 7: @22:34 Two affine grids and 2 sets of basis vectors
pg 8: @27:13 change of basis vectors example
pg 9: @30:47 change of basis example continued; Main Problem of Linear Algebra (MPLA)
pg 10: @34:03 summary of previous example; (MPLA) General case in 1dim; (MPLA) General case in 2dim
pg 11: @40:32 questions; Exercise 1.1
pg 12: @41:42 Exercises 1.2-4. (THANKS to EmptySpaceEnterprise)
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .

WildLinAlg: A geometric course in Linear Algebra
This course by N J Wildberger presents a geometrical view to Linear Algebra, with a focus on applications. We look at vectors, matrices, determinants, change of bases, row reduction, lines and planes, polynomial spaces, bases and coordinate vectors, and much more!
We are aiming for a careful exposition with an orientation on conceptual understanding, applications, and explicit examples. There are quite a few problems to challenge the viewer. It is perfectly possible to learn Linear Algebra from scratch with this course. I suggest to go through the series at about one a week, keep notes, and do all the problems.

1: Introduction to Linear Algebra 43:31
2: Geometry with vectors 44:15
3: Center of mass and barycentric coordinates 48:11
4: Area and volume 56:03
6: Applications of 2x2 matrices 43:47
5: Change of coordinates and determinants 48:36
7: More applications of 2x2 matrices 55:13
8: Inverting 3x3 matrices 45:44
9: Three dimensional affine geometry 43:02
10: Equations of lines and planes in 3D 1:08:52
11: Applications of 3x3 matrices 53:36
12: Generalized dilations and eigenvalues 55:35
13: Solving a system of linear equations 49:13
14: More row reduction with parameters 49:13
15: Applications of row reduction (Gaussian elimination) I 41:38
16: Applications of row reduction II 57:14
17: Rank and Nullity of a Linear Transformation 1:01:09
18: The geometry of a system of linear equations 1:08:59
19: Linear algebra with polynomials 46:14
20: Bases of polynomial spaces 59:50
21: More bases of polynomial spaces 45:52
22: Polynomials and sequence spaces 1:00:49
23: Stirling numbers and Pascal triangles 58:45
24: Cubic splines (Bezier curves) using linear algebra 32:35
25: Cubic splines using calculus 41:42
26: Change of basis and Taylor coefficient vectors 50:31
27: Geometry with linear algebra 28:12
28: Dot products, Pythagoras' theorem, and generalizations 27:51
29: Applications of the dot product to planar geometry I 36:06
30: Applications of the dot product to planar geometry II 45:48
31: Circles and spheres via dot products I 41:58
32: Circles and spheres via dot products II 28:14
33: The relativistic dot product 35:46
34: Oriented circles and 3D relativistic geometry I 46:12
35: Oriented circles and relativistic geometry II 50:39
36: Energy, momentum and linear algebra 46:03
37: An elementary introduction to Special Relativity I 46:40
38: An elementary introduction to Special Relativity II 55:48
39: Length contraction, time dilation and velocity addition 1:00:40
40a: Relativistic dot products and complex numbers 38:06
40b: Relativistic dot products and complex numbers II 25:28
41: The chromatic algebra of 2x2 matrices I 32:14
42: The chromatic algebra of 2x2 matrices II 37:56

Linear Algebra 1 (2009-2010) by Jaber Abu Jawkhah (An-Najah National University)

# click the upper-left icon to select videos from the playlist

source: ANajahUni 2012年1月8日
Lecture by Dr. Jaber Abu Jawkhah
Course: Linear Algebra 1
Department: Mathematics
Faculty: Faculty of Science
E-learning Website: http://videos.najah.edu/
Complete Playlist for the Course: http://www.youtube.com/playlist?list=...
An-Najah National University: http://www.najah.edu/
An-Najah National University Channel on YouTube: http://www.youtube.com/najahuniv

Lecture 1 46:47
Lecture 2 51:52
Lecture 3 50:43
Lecture 4 51:01
Lecture 5 51:19
Lecture 6 48:12
Lecture 7 52:09
Lecture 8 52:10
Lecture 9 47:48
Lecture 10 50:54
Lecture 11 49:36
Lecture 12 51:02
Lecture 13 50:31
Lecture 14 46:52
Lecture 15 53:10
Lecture 16 53:36
Lecture 17 49:49
Lecture 18 51:38
Lecture 19 45:39
Lecture 20 50:40
Lecture 21 52:10
Lecture 22 53:26
Lecture 23 51:38
Lecture 24 50:18
Lecture 25 52:37
Lecture 26 50:10
Lecture 27 53:27
Lecture 28 50:25
Lecture 29 50:54
Lecture 30 48:46
Lecture 31 52:05
Lecture 32 54:29
Lecture 33 47:48
Lecture 34 45:45
Lecture 35 53:35
Lecture 36 44:00
Lecture 37 48:34
Lecture 38 48:02
Lecture 39 51:49
Lecture 40 47:35
Lecture 41 51:22