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
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