A non-commutative algorithm for multiplying 5x5 matrices using 99 multiplications

Abstract

We present a non-commutative algorithm for multiplying 5 × 5 matrices using 99 multiplications. This algorithm is a minor modification of Makarov's algorithm which exhibit the previous best known bound with 100 multiplications.

The Tensor Rank of 5x5 Matrices Multiplication is Bounded by 98 andIts Border Rank by 89

“…Pursuing the works done the last 53 years in [18][19][20]22], we propose a new non-commutative algorithm for multiplying 5 × 5 matrices using 98 multiplications. More precisely, by presenting explicit algorithms, we establish the following result: Theorem 1.1.…”