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Numerical Linear Algebra Pages

An outline of your first linear algebra course (could skip)

A first look at programming

Good code? (could skip)

A first look at Matlab programming

Matlab function subroutine

Finite Precision Floating Point Arithmetic

Floating point representation

Comparing numbers

The floating point line pics

The floating point plane pic

Floating point Arithmetic

Floating point addition can be dangerous

Floating point dot product

Some Matrix Mechanics and Linear Algebra

Counting flops

Don't make it complicated (Does Ax=b have solutions?)

Matrix Multiplication

SOB (Standard Ordered Basis)

Coordinates (could skip)

Triangular Systems

Vector Norms

Matrix Norms

Singular Value Decomposition

Gaussian Elimination and Conditioning

Gaussian Elimination as a Matrix Factorization

The Gaussian Elimination Process

Gaussian Elimination with Partial Pivoting

Errors in Gaussian Elimination

The Ax=b residual vector

Linear system example

Condition analysis

Conditioning and Stability

A = LDMT and A = LDLT = AT (could skip)

Linear Least Squares

Inner Products

Orthogonal Projections

Normal Equations

Cholesky Factorization

Sensitivity of LS

Sensitivity of LS Details (could skip)

Solving the Normal Equations

Gram Schmidt QR

Classical Gram Schmidt vs Modified Gram Schmidt

Least Squares and MGS

GSPuzzle

Householder Reflectors

Householder QR Factorization

Householder Factored-Q Action

Thin QR and Full QR

Plots of LS polynomial fits

Eigenvalues

(slightly) Abstract Eigenstuff (could skip)

Concrete Eigenstuff (could skip)

The Power Method

The Inverse Power Method

The Sensitivity of Eigenvalues

Convergence of Eigenvectors

Hessenberg Matrices

Arnoldi (could skip)

QR Iterations

The Francis QR Step