Carl Meyer

MA 723

Course Outline


5. Norms, Inner Products, and Orthogonality

5.1 Vector Norms

5.2 Matrix Norms

5.3 Inner Product Spaces

5.4 Orthogonal Vectors

5.5 Gram-Schmidt Procedure

5.6 Unitary and Orthogonal Matrices

5.7 Orthogonal Reduction

5.8 Discrete Fourier Transform

5.9 Complementary Subspaces

5.10 Range-Nullspace Decomposition

5.11 Orthogonal Decomposition

5.12 Singular Value Decomposition

5.13 Orthogonal Projection

5.14 Why Least Squares?

5.15 Angles Between Subspaces

6. Determinants (Review)

6.1 Determinants

6.2 Additional Properties Of Determinants

7. Eigenvalues and Eigenvectors

7.1 Elementary Properties of Eigensystems (review)

7.2 Diagonalization by SimilarityTransformations (review)

7.3 Functions of Diagonalizable Matrices (review)

7.4 Systems Of Differential Equations

7.5 Normal Matrices

7.6 Positive Definite Matrices

7.7 Nilpotent Matrices and Jordan Structure

7.8 Jordan Form

7.9 Functions of Nondiagonalizable Matrices

7.10 Difference Equations, Limits, and Summability

7.11 Minimum Polynomials and Krylov Methods

8. Perron-Frobenius Theory of Nonnegative Matrices

8.1 Introduction

8.2 Positive Matrices

8.3 Nonnegative Matrices

8.4 Stochastic Matrices and Markov Chains