Numerical Methods for Solving Large Scale Eigenvalue Problems

This is more advanced level content,  which i learned in order to implement the QR algorithm that perform eigenvector decomposition and singular value decomposition

Link: http://people.inf.ethz.ch/arbenz/ewp/Lnotes/chapter3.pdf

Applied Numerical Computing

This is a freely downloadable ebook by Professor L. Vandenberghe. Very nice book for developers interested in implementing linear algebra algorithms. I primarily used to book for implementing my routines on QR factorization and Cholesky factorization to solve linear equations, least square problems data fitting, least-norm problem, and matrix inversion. But the book contains much more such as linear and nonlinear optimization

Link: http://www.seas.ucla.edu/~vandenbe/ee103.html

Online Course: Coding the Matrix: Linear Algebra through Computer Science

It took me twice to go through the lectures in this course to finally figure out why and how to obtain the orthogonal basis for the null space of a matrix and perform QR factorization to solve linear equations. But finally I was able to implement my own version of a linear algebra library for the first time which includes gaussian elimination, QR factorization, orthogonalization, determinant computation, backward substitution and various ways to obtain the basis for vector space, as well as some methods in least square regression. The examples given in the lecture are particularly practical and eye-opening on what linear algebra can do in image processing and security such as GF(2)

Link: https://www.coursera.org/course/matrix