These are some of my lecture notes on Math 511. They mostly follow the
book of Strang. They are edited and do not exactly reflect what was
actially said in each lecture. They are more concise than the book, and
I hope the statements are more precise and complete. Every statement
is formally proved (unless explicitly stated otherwise). Perhaps some
students will find them helpful. They have few solved exercises, because
there are plenty of them in Strang'a book.
I will be grateful to students who inform me about misprints or mistakes
in these notes.
Row operations and multiplication of matrices
Four subspaces associated to a matrix
Examples of linear transformations and operators
Orthogonal projections and least squares
Construction of orthogonal systems: Gram-Schmidt Process and QR-factorization
Complex numbers and Fast Fourier Transform
Spectral theorem for Hermitian and unitary matrices
Matrices with non-negative entries
Hermitian, unitary and normal matrices