Linear Algebra

1.

Subspaces, bases, dimension

2.

Linear transformations and matrix representations

3.

Linear functionals, adjoints, and dual spaces

4.

Scalar products and orthogonality

5.

Symmetric, hermitian, and unitary operators

6.

Eigenvectors and eigenvalues (spectral theorem)

7.

Jordan canonical form

References:

1.

Sh. Adler, Linear Algebra Done Right, Springer-Verlag.

2.

M. L. Curtis, Abstract Linear Algebra, (skip Chapter 2 (B) and Chapter 5), (Springer-Verlag).

3.

K. Huffman and R. Kunze, Linear Algebra, (skip Chapters 4, 5, Sections 6.5, 7.2, 7.6, 7.5, 9.4, 9.6, 10.6), (Prentice-Hall).

4.

S. Lang, Linear Algebra, Third Edition, (Springer-Verlag).

Note: Material skipped in one of these references might be found in other references, but presented in a more elementary form.