My question takes a little bit of preamble: it concerns a well-known and solved problem, but I am looking for a solution with a particularly nice property. $\newcommand{\matrix}[4]{\left( \begin{array}{cc} #1 & #2 \\ #3 & #4 \end{array} \right)} \DeclareMathOperator{\lcm}{lcm}$In using Guassian elimination to put a matrix into Smith normal form over $\mathbb{Z}$ (or, more generally, […]

I am currently taking a intro course to abstract algebra and am revisiting ideas from linear algebra so that I can better understand examples. When i was in undergraduate learning L.A., I thought of matrix manipulations as ways of solving $n \times n$ systems of equations. Recently i was exposed to the idea of a […]

Gauss-Jordan elimination is a technique that can be used to calculate the inverse of matrices (if they are invertible). It can also be used to solve simultaneous linear equations. However, after a few google searches, I have failed to find a proof that this algorithm works for all $n \times n$, invertible matrices. How would […]

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