Or even a semi-group: Integer matrices whose entries are all divisible by 2 are closed under matrix multiplication, or indeed, divisible by any n, for n>=1. Also, Markov/stochastic matrices are closed under matrix multiplication. At 07:38 AM 9/8/2017, Veit Elser wrote:
A stronger condition is that the matrices form a group.
For example, consider the largest group of matrices (of a particular size) where all matrix elements are non-negative.
-Veit
On Sep 7, 2017, at 10:53 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Thanks, Victor!
The article looks quite interesting, but also quite tough sledding...
At the topmost level, are there any classes of matrices other than upper triangular, lower triangular, both/diagonal, and/or block versions of same, that preserve the overall pattern of zeros?
From a directed graph adjacency matrix perspective, triangular matrices are partial orders forced into a linear order; block matrices have subsets of vertices with cyclic orders (equivalence classes).
It seems to me that these might exhaust the classes of matrices with patterns of zeros.