A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. They are a crucial part of linear algebra and have various applications in fields like engineering, ...

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 ...

Some algorithms based upon a projection process onto the Krylov subspace $K_m = \operatorname{Span}(r_0, Ar_0, \ldots, A^{m - 1}r_0)$ are developed, generalizing the ...

The goal of this assignment was to develop a program in C that is capable of solving first-order linear systems of equations. These systems are of the form Ax=b, where A is a known matrix, b is a ...

Our informal method of solving linear systems is to do certain manipulations to the equations until they are in a form where the solutions are easy to read off. This method only works if the ...

We associate a sequence of Toeplitz matrices with the rational formal power series $T(z)$. An algorithm for solving linear equations with a Toeplitz matrix from this ...