The tensor rank of 5x5 matrices multiplication is bounded by 98 and its border rank by 89

no code implementations • 29 Jan 2021 • Alexandre Sedoglavic, Alexey V. Smirnov

We present a non-commutative algorithm for the product of 3x5 by 5x5 matrices using 58 multiplications.

Computational Complexity

Some fast algorithms multiplying a matrix by its adjoint

no code implementations • 4 Jan 2021 • Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic

We present a non-commutative algorithm for the multiplication of a 2 x 2 block-matrix by its adjoint, defined by a matrix ring anti-homomorphism.

Symbolic Computation