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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