2270 Chapter 6 Lecture Topics S2018

Updated: 09 Apr 2018   Today: 31 Mar 2023
  1. Invertible Matrices
  2. Invertible Matrix Theorem: All parts a to x from the textbook
  3. Independence Tests and Subspaces
  4. Independence tests: Rank, Determinant, Sampling, Wronskian, Geometry
    Vector Models and Vector Spaces
  5. Eigenanalysis Selected Topics
  6. 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.
  7. Cayley-Hamilton Theorem
  8. Slides: cayleyHamilton.pdf, Cayley-Hamilton Theorem, Examples
    Slides: deSystemsCayleyHamilton.pdf, Cayley-Hamilton Theorem, Differential equations
    Slides: orthogonality.pdf, inner product, orthogonal sets, Cauchy-Schwartz inequality, triangle inequality
    Slides: fundTheoremLinearAlgebra.pdf, Orthogonal subspace W-perp, Four Fundamental subspaces, Fundamental Theorem of Linear Algebra
  9. Advanced Topics in linear Algebra
  10. 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