\[
U^{-1}\begin{pmatrix}-1&1&0&0&0\\-9&5&0&0&0
\\1&0&1&1&0\\-5&11&-3&-5&1
\\124&-20&-8&-9&1\end{pmatrix}U=
\begin{pmatrix}2&1&0&0&0\\0&2&0&0&0\\
0&0&-1&1&0\\0&0&0&-1&1\\0&0&0&0&-1\end{pmatrix}
\]
Advanced Linear Algebra
(Math 403)
Spring 2020
Instructor:
Paul Aspinwall
Credits: 1.00, Hours: 03.0
Time: MW 1:25PM - 2:40PM
Location: Physics 119
Requirements
Prerequisits
Math 222 (or 212) and Math 221 (or 218), or consent from me.
Homework
is here. It is given weekly.
Notes
Exams
- Midterm 1: February 17
- Final Exam: Friday May 1, 2:00-5:00PM
Synopsis
Topics will include (amongst others)
- Vector spaces over arbitrary fields, subspaces and quotients
- Duality and inner products
- Jordan normal form and the Cayley Hamilton Theorem
- Self-Adjoint Operators
- The spectral theorem and normal operators
- The Rayleigh Quotient and Heisenberg's Uncertainty Principle
- Singular value decomposition and Data Compression
- Principal component analysis
- Positive Matrices, Perron's theorem
- Markov chains
- Tensor products and exterior algebras
- Matrix Groups and Lie Algebras
- Convexity
Textbooks
- Peter D. Lax, Linear Algebra and its Applications, Second Edition, Wiley 2007.
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