Time and location:
| Date | Topic | Lecture notes |
|---|---|---|
| February 25 | Dot product, inner product. Cauchy-Schwarz inequality. | lecture notes |
| March 2 | Norm and orthogonality. Orthonormal basis, Gram-Schmidt orthogonalization. | lecture notes |
| March 3 | Othogonal complement and projection. | lecture notes |
| March 17 | Method of least squares, pseudoinverse. Isometries and orthogonal matrices. | lecture notes |
| March 24 | Determinants - definition, row operations. | lecture notes |
| April 6 | Determinants - multiplicativity, linear equations, inverse. | lecture notes |
| April 7 | Applications of determinants. Eigenvalues and eigenvectors. | lecture notes |
| April 14, April 21 | Matrix similarity. Diagonalization and Jordan normal form. | lecture notes |
| April 28 | Cayley-Hamilton theorem. Symmetric and positive matrices, Perron-Frobenius theorem. | lecture notes |
| May 5, May 12 | Bilinear and quadratic forms. Classification of quadrics. | lecture notes |
| May 19 | Positive (semi)definiteness. | lecture notes |
| May 26 | Matrix decompositions. | lecture notes |