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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
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