Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

Gaussian Elimination The general procedure learned to solve a system of linear equations is Gaussian elimination. The goal is to apply row operations to "eliminate" all the variables except for one in ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

Several decompositions of symmetric matrices for calculating inertia and solving systems of linear equations are discussed. New partial pivoting strategies for decomposing symmetric matrices are ...

We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first finds a short vector ...

The most famous quantum linear system solving algorithm is the Harrow-Hassidim-Lloyd (HHL) algorithm, which accelerates the solution of linear systems through quantum superposition and interference.