Syllabus

Date Notes Topics
May 1 Brief review of matrix algebra
May 6 Review of gaussian elimination and elementary matrices
May 8 Right, left, and two-sided inverses
May 13 LU factorization
May 15 Inner products, norms, and orthogonality
May 20 Matrix norms
May 22 Orthogonal complement, projection
May 27 Projections (cont.), Gram–Schmidt algorithm
May 29 Review of eigenvectors and eigenvalues
Jun 3 Orthogonal diagonalization
Jun 5 Positive definite matrices, Cholesky factorization
Jun 10 QR factorization
Jun 12 Computing/estimating eigenvalues
Jun 17 Gershgorin circle theorem
Jun 19 Midterm test
Jun 24 Singular value decomposition
Jun 26 Singular value decomposition (cont.), generalized inverses
Jul 3 Schur canonical form
Jul 8 Spectral theorem, Cayley–Hamilton theorem
Jul 10 Jordan form
Jul 13 Quadratic forms
Jul 15 Rayleigh's principle
Jul 17 Min-max principle
Jul 22 Review