Math 20610 Linear Algebra (Fall 2023)
Linear Algebra
| Date | Lecture | Topics | Textbook |
| Wed 08/23 | 1 | Overview | |
| Fri 08/25 | 2 | Vectors, rotations, algebraic operations | 1.1 |
| Mon 08/28 | 3 | Scalar multiplication of vectors, geometric applications | 1.1 |
| Wed 08/30 | 4 | Real vector spaces, examples | 2.1 |
| Fri 09/01 | 5 | Span and null space examples of real vector spaces | 3.2 |
| Mon 09/04 | 6 | Dot product, angles, orthogonality, projections | 1.2 |
| Wed 09/06 | 7 | Orthogonality and projections | 1.2 |
| Fri 09/08 | 8 | Solving linear systems and soccer balls | 1.4 |
| Mon 09/11 | 9 | Solving linear systems | 1.4 |
| Wed 09/13 | 10 | Solving linear systems | 1.5 |
| Fri 09/15 | 11 | Echelon forms: proof they exist, applications | 1.4 |
| Mon 09/18 | 12 | Applications of echelon forms: projections, curve fitting, partial fractions | 1.6 |
| Wed 09/20 | 13 | Linear transformations | 4.4 |
| Fri 09/22 | 14 | Matrix of a linear transformation, rotations | 4.3 |
| Mon 09/25 | 15 | Matrix of linear transformation, abstract example | 2.2 and 4.3 |
| Wed 09/27 | 16 | Image of linear transformation | 1.5 and 4.4 |
| Fri 09/29 | 17 | Compositions of linear transformations and matrix multiplication | 2.1 and 2.2 |
| Mon 10/02 | 18 | Matrix multiplications and trig identities, inverse matrices | 2.1 and 2.2 |
| Wed 10/04 | 19 | Inverse matrices and solving linear equations | 2.3 |
| Fri 10/06 | 20 | Elementary matrices and Gaussian elimination | 2.4 |
| Mon 10/9 | 21 | Matrix algebra, upper and lower triangular matrices | 2.4 |
| Wed 10/11 | 22 | Midterm | |
| Fri 10/13 | 23 | Elementary matrices and the LU decomposition | 2.4 |
| Mon 10/23 | 24 | Dimension | 3.4 |
| Wed 10/25 | 25 | Linear independence | 3.3 |
| Fri 10/27 | 26 | Dimension inequalities | 3.4 |
| Mon 10/30 | 27 | Kernel, image, rank: dependent and independent variables | 3.2 |
| Wed 11/01 | 28 | Applications to projection and orthogonality | 2.5 |
| Fri 11/03 | 29 | Row and column spans | 3.2 |
| Mon 11/06 | 30 | Orthogonal complements | 3.2 |
| Wed 11/08 | 31 | Transpose matrices and dot product as matrix multiplication | 2.5 and 4.1 |
| Fri 11/10 | 32 | Isometries and orthogonal matrices, symmetric and skew-symmetric matrices | 4.2 |
| Mon 11/13 | 33 | Orthogonal and orthonormal bases, the Gram-Schmidt procedure | 4.2 |
| Wed 11/15 | 34 | Matrix of projection, matrix of a linear transformation in a different basis | 4.3 |
| Fri 11/17 | 35 | Change of basis formula for the matrix of a linear transformation | 4.3 |
| Mon 11/20 | 36 | Determinants and volumes, properties of determinants | 5.1 and 5.3 |
| Mon 11/27 | 37 | Determinants and cofactors | 5.2 |
| Wed 11/29 | 38 | Cramer's rule and determinants | 5.2 |
| Fri 12/01 | 39 | Eigenvalues and eigenvectors | 6.1 |
| Mon 12/04 | 40 | Characteristic polynomials and eigenvalues | 6.1 |
| Wed 12/06 | 41 | Diagonalization | 6.2 |
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