Fundamentals of Linear Algebra and Optimization

This note covers the following topics: Vector Spaces, Bases, Linear
Maps, Matrices and Linear Maps, Direct Sums, Affine Maps, The Dual Space,
Duality, Gaussian Elimination, LU, Cholesky, Echelon Form, Determinants, Vector
Norms and Matrix Norms, Eigenvectors and Eigenvalues, Iterative Methods for
Solving Linear Systems, Euclidean Spaces, Hermitian Spaces, Spectral Theorems,
The Finite Elements Method, Singular Value Decomposition and Polar Form,
Applications of SVD and Pseudo-Inverses, Annihilating Polynomials, Differential
Calculus, Schur Complements and Applications, Linear Programming and Duality,
Hilbert Spaces, Soft Margin Support Vector Machines.

**Author(s):** Jean Gallier and Jocelyn
Quaintance

925 Pages