(1) Vector spaces and subspaces; Linear transformations; Matrix multiplication and inversion
(2) Row echelon forms; Nullspace and Range; Solutions of linear systems; Rank normal
form; Four fundamental subspaces
(3) Linear independence, basis, dimension, rank and nullity theorem
(4) Linear transforations
(5) Change of basis, similarity
(6) Real and complex inner product spaces, orthogonal vectors
(7) Gram-Schmidt orthogonalization process
(8) Unitary and orthogonal matrices
(9) Complementary subspaces
(10) Orthogonal decomposition
(11) Determinants [Not covered in this course, just here for background]
(12) Eigensystems
(13) Diagonalization
(14) Spectral theorem for normal matrices
(15) Details of proof of Spectral theorem for normal matrices
(16) Matrix Exponentation and Systems of ODE's
(17) Quadratic forms and positive definite matrices
[Not covered in this course, just here in case you are interested]
(18A) Calculus Facts for Fourier Series Calculations
(18B) Fourier Series I: Trigonometric Fourier Series
(19A) Fourier Series II: Pointwise Convergence
(19B) Fourier Series II: Pointwise Convergence and Gibbs phenomenon
(20) Fourier Series III: Scaling and Complex Fourier Series
(21) Fourier Series IV: Uniform Convergence, Differentiation and Integration Theorems
(22) Discrete Fourier transform
(23) Filtering and Convolution
(24) Proof of Pointwise Convergence Theorem