2270 Chapter 5 Lecture Topics S2019

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: Introduction to eigenanalysis Historical introduction to the subject of eigenvalues and eigenvectors for matrices. Algebraic eigenanalysis, computation and diagonalization (October 2016).
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.
TXT: Larry Page's Google algorithm, Where to find a simple explanation of Page's Page-Rank algorithm.
3. Cayley-Hamilton Theorem
Slides: deSystemsCayleyHamilton.pdf, Cayley-Hamilton Theorem, Examples
4. Jordan Form and Eigenanalysis
Manuscript: jordan-form.pdf, Jordan theory, Jordan Form, AP=PJ, Real Jordan form, map a+ib ==> 2x2 matrix, Exponential matrices.
5. Commutative Diagram
PDF: commutativeDiagram.pdf, Rule for forming composition of maps in a commutative diagram, as found in section 5.4: Matrix of a linear transformation, pae 291.