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MAT 3341

Applied Linear Algebra

3 units

Library resources

Winter 2024

Topics

  • Solving linear systems through elimination and LU factorization
  • Inner products, vector and matrix norms, and conditioning
  • Positive definite matrices and Cholesky factorization
  • Orthogonal bases, QR factorization and projections
  • Least-squares minimization
  • Eigenvalue computation and diagonalization
  • Jordan form, singular-value decomposition and pseudoinverses

Readings

  • Applied Linear Algebra
    Peter J. Olver; Chehrzad Shakiban · 2nd edition, Springer, 2018 · Textbook
Spring/Summer 2019

Topics

  • Matrix factorizations: LU, QR, Cholesky and Schur
  • Norms, sensitivity and conditioning
  • Eigenvalue estimation and Gershgorin discs
  • Singular-value decomposition and pseudoinverses
  • Principal components
  • Jordan form and matrix exponentials
  • Quadratic forms, Rayleigh quotients and min–max principles

Readings

  • Linear Algebra with Applications
    W. Keith Nicholson · Recommended open reference
  • A First Course in Linear Algebra
    Kenneth Kuttler; Lyryx · Recommended open reference
  • Linear Algebra Done Wrong
    Sergei Treil · Recommended open reference
  • Linear Algebra
    David Cherney; Tom Denton; Rohit Thomas; Andrew Waldron · Recommended open reference
  • Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares
    Stephen Boyd; Lieven Vandenberghe · Recommended open reference
  • Lecture notes / supplementary course reference
Sources