The secret life of matrix factorizations: how matrix decompositions reveal and keep secrets of linear equations and what we can do about it. (arXiv:2304.12451v1 [math.NA])

This paper explores the relationship between matrix factorizations and linear
matrix equations. It shows that every matrix factorization defines two hidden
projectors, one for the column space and one for the row space of a matrix, and
how to calculate them. The projectors can be applied to solve linear matrix
equations, generate low-rank approximations, or design randomized matrix
algorithms. But also, as demonstrated, they can be applied in cryptography to
encrypt and decrypt messages. The paper discusses some of the …

algorithms column cryptography decrypt design encrypt hidden life low math matrix messages relationship secret secrets space