2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107914An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a vector in ${\cal O}(N)$. This is in contrast to the usual ${\cal O}(N^3)$ and ${\cal O}(N^2)$. A finite size bit register can lead to speeds up of an order of magnitude in large matrices such as $500\times 500$. The FFT can be improved from ${\cal O}(N\ln N)$ to ${\cal O}(N)$ steps, or even fewer steps in a modified butterfly configuration.6 pages, LaTeXGeneral Physicstext