# Generalized Bruhat decomposition in commutative domains

## TL;DR

This paper introduces deterministic recursive algorithms for computing generalized Bruhat decompositions of matrices over commutative domains, matching the complexity of matrix multiplication.

## Contribution

It presents a novel recursive algorithm for generalized Bruhat decomposition in commutative domains with optimal complexity.

## Key findings

- Algorithm has the same complexity as matrix multiplication.
- Provides a deterministic recursive approach.
- Applicable to matrices over commutative domains.

## Abstract

Deterministic recursive algorithms for the computation of generalized Bruhat decomposition of the matrix in commutative domain are presented. This method has the same complexity as the algorithm of matrix multiplication.