Applied Linear Algebra

· Syllabus

· Review Sheet

Homework List

· Homework List 2009 (Mathematica Format)

· Homework List 2009 (pdf Format)

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· Homework List (pdf format)

· Homework List (previous years)

Homework Solutions

· Homework 1 Block Multiplication

· Homework 2 Stochastic Matrices, Traces

· Homework 2 Determinants

· Homework 4 Determinants

· Homework 5 Determinants of Tridiagonal Matrices

· Homework 6 Determinants, Binet-Cauchy, Cauchy-Schwarz

· Homework 7 LU factorization, Vandermonde

· Homework 8 Hadamard's Inequality

· Homework 9 Vector Space Axioms

· Homework 10 Image and kernel

· Homework 11 General Solution of Linear Equations

· Homework 12 Change of Basis

· Homework 13 Gram-Schmidt

· Homework 14 Gramian

· Homework 15 Householder Matrix, Tridiagonal Form

· Homework 16 Legendre Polynomials

· Homework 17 Linear Transformations

· Homework 14 Projections

· Homework 19 Chebyshev Polynomials, Circulants, Tridiagonals

Handouts

Laplace Formula for determinants

Permutations

Determinants
Determinants (pdf format)
Cholesky Factorization

LU factorization

Householder Matrices

Given Matrices

Projections

QR Factorization

Gram-Schmidt Applications - Fit, Overdetermined, Undetermined Systems

Change of Basis

Schur’s Unitary Triangularization Lemma

Curvature of a Surface

Leverrier’s Algorithm

Cramer’s Rule and the Adjugate Matrix

The Cayley-Hamilton Theorem

Coefficients of the Characteristic Polynomial

Principal Axis Theorem

Singular value Theorem

Data Import

Jordan Form

Matrix Polynomials Summary

Eigenvalue Techniques

Vector Space and Matrix Norms

Spectral Radius

Gersgorin’s Theorem

Holomorphic Functions

Positive Matrices (Perron Frobenius Theory)

Fourier Transforms

Rank + Nullity

Linear Independence

Homogeneous Systems

Minimal Spanning Sets

Row and Column Space

Computer Routines and Software

· <<myLAPackage`