2270 Chapter 5 Lecture Topics S2016

1. Eigenanalysis, what is it?
Slides: Whatseigenanalysis.pdf, Eigenpairs, Eigenvalues, Eigenvectors explained, Fourier's eigenanalysis model, Data conversion example, Powers computed by eigenanalysis, History of Fourier's model (1822), Characteristic equation, Computing eigenpairs, Independence of eigenvectors.
2. Eigenanalysis
Manuscript: eigenanalysisI.pdf, Eigenanalysis, History, Fourier's method, Diagonalization and AP=PD, Fourier's 1822 heat model, Examples for 2x2, 3x3 eigenpairs, diagonalization and AP=PD computation.
Manuscript: eigenanalysisII.pdf, Discrete dynamical systems, Stochastic matrices, Eigenanalysis and footballs, Ellipse and eigenanalysis, Coordinate rotation.
Slides: algebraicEigenanalysis2008.pdf, Algebraic theory for eigenpairs, Algorithm, AP=PD and diagonalization, Examples 2x2 and 3x3.
3. Cayley-Hamilton Theorem
Slides: deSystemsCayleyHamilton.pdf, Cayley-Hamilton Theorem, Examples
4. Advanced Topics
Manuscript: advancedTopicsLinearAlgebra.pdf, Jordan's Theorem, Diagonalization, Jordan Normal Form, Symmetric matrices and Orthogonality, Gram-Schmidt, Near Point Theorem, QR-decomposition, Least Squares, Spectral Theorem, Schur's Theorem, Singular Value Decomposition, Geometry of SVD, Four Fundamental subspaces and SVD