Optimize Matrix Multiplication in DPGL(n, p) Using Permutation Composition and Diagonal Element-wise Multiplication

[aidevnn]

The current matrix multiplication implementation in the DPGL(n, p) class (Diagonal by Permutation matrices) can be made more efficient. Instead of performing standard matrix multiplication, the process can be optimized by composing the permutation components and multiplying the diagonal elements term-by-term. This approach would significantly reduce computational complexity and improve performance for matrices in this class.

[aidevnn]

The group of Diagonal by Permutation matrices referenced in this issue is formally known as the Monomial Group in group theory and is defined as the subgroup of the general linear group GL(n,p) composed of all invertible matrices that can be expressed as the product of a diagonal matrix and a permutation matrix, and it is desribed in Øystein Ore’s paper, “Theory of Monomial Groups” (AMS, 1938).