## 2017-08-31

### Linear Algebra (Spring 2016) by James Cook

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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