Sections

Brief Description

Week 1

1.2, 1.3, 1.4, 1.5

Intro to proofs and vectors spaces, linear dependence and linear independence.

Week 2

1.6, 2.1, 2.2, 2.3

Bases and dimension. Linear transformations, matrix representations of linear transformations.

Week 3

2.4, 2.5, 2.6, 3.1

Isomorphisms. Change of coordinate matrix, dual spaces. Elementary Matrices.

Week 4

3.2, 3.3, 3.4, 4.1-4.2

Rank of a matrix, matrix inverses, systems of linear equations. Determinants.

Week 5

4.2-4.4, 5.1, 5.2

Determinants, Eigenvalues and eigenvectors, diagonalizability.

Week 6

5.4, 6.1, 6.2

Cayley-Hamilton Theorem, Inner producs and Norms, Gram-Schmidt orthogonalization Process

Week 7

6.3, 6.5

The adjoint of a linear operator, unitary and orhogonal operators.

Week 8

6.6, 6.7

Orthogonal projections and spectral theorem, bilinear and quadratic forms.

Week 9

7.1

Jordan Canonical Form.

Week 10

7.2, 7.3

Jordan Canonical Form, Minimal polynomial.