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

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

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 …