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Math 3406 - Fall 2017 A Second Course on Linear Algebra Howard (Howie) Weiss |
Lecture Schedule
8/22 Introduction, key facts about matrix multiplication, 4 ways to view matrix multiplication, upper/lower trangular (UT/LT) matrices, solving Ax=b for an UT matrix, review of Gauss Elimination
8/24 Gauss Elimination, LU decomposition, permutation matrices, pivots
8/29 PA=LDU decomposition, computational cost of LU decomposition, inverses
8/31 Gauss-Jordan algorithm to compute matrix inverse, transpose and properties, symmetric matrices
9/5 Linear regression (example of Ax=b), vector spaces and their subspaces
9/7 Matlab for linear systems demo, null space and column space of a matrix, Echelon form of a matrix
9/12 Campus closed
9/14 Reduced form of a matrix and using it to compute the null and column spaces
9/19 Independence of vectors, bases, dimension
9/21 Exam 1
9/26 The 4 fundamental subspaces and the Fundamental Theorem of Linear Algebra I, Rank theorem
9/28 Existence and uniqueness of solutions of Ax=b, left and right inverses, rank-1 matrices, linear transformations
10/3 Linear transformations including differentiation and integration on polynomials, matrix representation of a linear transformation
10/5 Inner products and orthogonality, Fundamental theorem of orthogonality, Fundamental Theorem of Linear Algebra II, Fredholm's alternative, projection matrices
10/12 Orthogonal projection, best approximate solution to Ax=b, projection matrices
10/14 Orthonormal matrices: examples and properties, Gram-Schmidt Algorithm
10/16 Applications of Gram-Schmidt to approximation of functions: Legendre polynomials and Fourier series
10/24 QR decomposition, determinants
10/26 Determinants, eigenvalues and eigenvectors
11/02 Exam 2
11/07 Diagnonalization, matrix powers, Leslie population model, linear systems of ODEs
11/09 Linear systems of ODEs, Markov chains, introduction to spectral theorem for symmetric matrices
11/14 Quick review of complex numbers, complex matrices, examples
11/16 Hermitian matrices, spectral theorem for real, self-adjoint matrices, Perron-Frobenius theorem
11/21 Unitary matrices, simularity transformations, change of basis formula
11/23 Thanksgiving break
11/28 Schur's lemma and applications, normal matrices, diagonalization
11/30 SVD
12/01 Applications of SVD: JPEG image compression and PCA
8/24 Gauss Elimination, LU decomposition, permutation matrices, pivots
8/29 PA=LDU decomposition, computational cost of LU decomposition, inverses
8/31 Gauss-Jordan algorithm to compute matrix inverse, transpose and properties, symmetric matrices
9/5 Linear regression (example of Ax=b), vector spaces and their subspaces
9/7 Matlab for linear systems demo, null space and column space of a matrix, Echelon form of a matrix
9/12 Campus closed
9/14 Reduced form of a matrix and using it to compute the null and column spaces
9/19 Independence of vectors, bases, dimension
9/21 Exam 1
9/26 The 4 fundamental subspaces and the Fundamental Theorem of Linear Algebra I, Rank theorem
9/28 Existence and uniqueness of solutions of Ax=b, left and right inverses, rank-1 matrices, linear transformations
10/3 Linear transformations including differentiation and integration on polynomials, matrix representation of a linear transformation
10/5 Inner products and orthogonality, Fundamental theorem of orthogonality, Fundamental Theorem of Linear Algebra II, Fredholm's alternative, projection matrices
10/12 Orthogonal projection, best approximate solution to Ax=b, projection matrices
10/14 Orthonormal matrices: examples and properties, Gram-Schmidt Algorithm
10/16 Applications of Gram-Schmidt to approximation of functions: Legendre polynomials and Fourier series
10/24 QR decomposition, determinants
10/26 Determinants, eigenvalues and eigenvectors
11/02 Exam 2
11/07 Diagnonalization, matrix powers, Leslie population model, linear systems of ODEs
11/09 Linear systems of ODEs, Markov chains, introduction to spectral theorem for symmetric matrices
11/14 Quick review of complex numbers, complex matrices, examples
11/16 Hermitian matrices, spectral theorem for real, self-adjoint matrices, Perron-Frobenius theorem
11/21 Unitary matrices, simularity transformations, change of basis formula
11/23 Thanksgiving break
11/28 Schur's lemma and applications, normal matrices, diagonalization
11/30 SVD
12/01 Applications of SVD: JPEG image compression and PCA