ACM 104
Linear Algebra

Instructor
Eric Chung
Office: Firestone 315
Phone: 626.395.4550
Office Hours: by appointment
Website: www.acm.caltech.edu/~tschung
Email: tschung@acm.caltech.edu

TA
Stephen Becker
Office: Firestone 214
Office Hours: Thursday 4:00-5:00p
Email: srbecker@acm.caltech.edu

Schedule
Date and Time: MF 2:30-3:25p, W 4:00-4:55p
Location: Baxter 237

Textbook
Linear Algebra. Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence
(Chapter 1-2,5-7)
Introductory Functional Analysis with Applications. Kreyszig
(Chapter 3 and 9)

Topics
Vector spaces, bases, Gram-Schmidt, linear maps and matrices, linear functionals, the transposed matrix and duality, kernel, image and rank, invertibility, triangularization, determinants and multilinear forms, powers of matrices and difference equations, the exponential of a matrix and ODEs, eigenvalues, Gershgorin disc theorem, eigenspaces, SVD, polar decomposition. Nilpotent-semisimple decomposition and the Jordan normal form. Symmetric hermitian and positive definite matrices, diagonalizability, unitary matrices, bilinear forms. Hilbert spaces, projections, Riesz theorem, Fourier series, spectrum, self-adjoint operators.

Grading
There will be weekly homework assignments throughout the quarter and a final exam. Grades will be assigned according to the following allocation.
HW: 40%
Final: 60%