Growth in products of matrices: fastest, average, and generic

arXiv:2405.00610v1 Announce Type: cross
Abstract: The problems that we consider in this paper are as follows. Let A and B be 2x2 matrices (over reals). Let w(A, B) be a word of length n. After evaluating w(A, B) as a product of matrices, we get a 2x2 matrix, call it W. What is the largest (by the absolute value) possible entry of W, over all w(A, B) of length n, as a function of n? What is the expected absolute …

arxiv call cs.cr growth length math.co math.gr math.pr matrix problems product products word