## 2017-08-31

### Linear Algebra (Spring 2015) by James Cook

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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