This is intended as a mini intro to some practical linear algebra.

- A detailed proof that the Rayleigh-Ritz quotient is maximized by the largest eigenvector: optimizationTutorial01.pdf
- Table of Contents:

- Linear Algebra: Bilinear Form - A Simple Optimization Problem
- Definitions
- Inner Product
- Quadratic Form and the Rayleigh-Ritz Quotient
- A real symmetric matrix has only real eigenvalues
- The eigenvectors of a real symmetric matrix form an orthonormal basis
- Spectral decomposition of a real symmetric matrix
- Equality of optimization of Rayleigh-Ritz quotient

- Analysis
- Dual Space
- Operator Norm
- Sets