# Fast generalized Bruhat decomposition

## TL;DR

This paper introduces a fast, deterministic, pivot-free recursive algorithm for generalized Bruhat decomposition and matrix inversion, matching matrix multiplication complexity and suitable for parallel computing systems.

## Contribution

It presents a novel recursive, pivot-free algorithm for generalized Bruhat decomposition with complexity comparable to matrix multiplication, optimized for parallel systems.

## Key findings

- Algorithm has the same complexity as matrix multiplication.
- Suitable for parallel computer systems.
- Efficient computation of matrix inverse.

## Abstract

The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as algorithm of matrix multiplication and it is suitable for the parallel computer systems.