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These notes are from my iPad using GoodNotes.
Day 1 -Motivation and Preliminaries; Complex Numbers; Vandermonde Matrices; Inner Products
Day 2 -Orthogonality and Orthonormality; Adjoints; Unitaries
Day 3 -Vector and Matrix Norms, Equivalence of Norms
Day 4 -Properties of Unitaries; Singular Value Decomposition (SVD)
Day 5 -Absolute Value and Polar Decomposition; Reduced and Full SVD
Day 6 -Consequences of SVD; Geometric Interpretation
Day 7 -Orthogonal Projections; Decomposition into Rank One's
Day 8 -Full and Reduced QR Decomposition via Gram Schmidt
Day 9 -Algorithms and Cost for QR Decomposition
Day 10 -More on Cost; Full and Reduced QR Decomposition via Householder Triangulation
Day 11 -Householder QR By Example
Day 12 -More on QR via Householder
Day 13 -Cost for Householder Triangulation; Cost by Picture
Day 14 -Least Squares
Day 15 -The Pseudoinverse; QR Decomposition and Least Squares; Polynomial Interpolation
Day 16 -Absolute and Relative Condition Numbers; The Jacobian and Conditioning
Day 17 -Well- and Ill-Conditioned Problems: Definitions and Examples
Day 18 -Machine Epsilon; Floating Point Arithmetic; Problems and Algorithms; Relative and Absolute Error; Backwards Stability
Day 19 -Examples of Backwards Stable Algorithms; Stability
Day 20 -Examples of Stable and Backwards Stable Algorithms; Backwards Stability and Conditioning
Day 21 -Algorithm for Householder QR; Solving Linear Equations via QR Decomposition
Day 22 -Algorithm for Back Substitution;
Day 23 -A Least Squares Example
Day 24 -Conditioning for Least Squares Problems;
Day 25 -More on Conditioning for Least Squares; Stability for Least Squares
Day 26 -More on Stability for Least Squares
Day 27 -Gaussian Elimination: LU Decomposition and Pivoting
Day 28 -Examples of Pivoting; Algorithm for Partial Pivoting and Flop Count; Backwards Stability of Algorithm
Day 29 -Diagonalizability; Geometric and Algebraic Multiplicity of Eigenvalues;Schur Factorization
Day 30 -Proof of Schur Factorization; Hessenberg Matrices; Iterative Eigenvalue Algorithms
Day 31 - More Eigenvalue Algorithms; Rayleigh Quotient; Power Iteration; Rates of Convergence
Day 32 -Rayleigh Quotient Iteration and Rate of Convergence
