2270 Chapter 6 Lecture Topics S2017

1. Eigenanalysis Selected Topics
Manuscript: eigenanalysis2016-manuscript.pdf, Introduction to eigenanalysis, basic theory, AP=PD, computational algorithm, diagonalization.
Manuscript: eigenanalysisII.pdf, Discrete dynamical systems, Stochastic matrices, Eigenanalysis and footballs, Ellipse and eigenanalysis, Coordinate rotation.

2. Cayley-Hamilton Theorem
Slides: cayleyHamilton.pdf, Cayley-Hamilton Theorem, Examples
Slides: deSystemsCayleyHamilton.pdf, Cayley-Hamilton Theorem, Differential equations
3. Advanced Topics in linear Algebra
Manuscript: advancedTopicsLinearAlgebra.pdf, Cayley-Hamilton proof, Jordan theory, Orthogonality and Least Squares, Gram-Schmidt, Orthonormal basis, Near Point Theorem, QR-Decomposition, Spectral Theorem, Schur's Theorem, Singular Value Decomposition, Geometry of the SVD, Four Fundamental Subspaces of Gilbert Strang