Strassen $2\times2$ Matrix Multiplication from a 3-dimensional Volume Form

TL;DR

This paper explores the derivation of Strassen's 2x2 matrix multiplication algorithm using the volume form on a specific 3-dimensional quotient space of matrices, providing a geometric perspective.

Contribution

It introduces a novel geometric interpretation of Strassen's algorithm through the volume form on a quotient space of matrices.

Findings

Provides a geometric derivation of Strassen's algorithm

Connects matrix multiplication to volume forms on quotient spaces

Offers insights into the algebraic structure of matrix algorithms

Abstract

The Strassen $2\times2$ matrix multiplication algorithm arises from the volume form on the 3-dimensional quotient space of the $2\times 2$ matrices by the multiples of identity.