On Sums of s-orthogonal Matrices

Abstract

In this paper we discussed the sum of s-orthogonal and s-unitary matrices. Also we show that every $A\in M_n(\mathbb{Z}_{2n-1})$ can be written as a sum of s-orthogonal matrices in $M_n$. Moreover, we show that every $A\in M_n(\mathbb{Z}_{2k})$ can be written a sum of of s-orthogonal matrices in $M_n(\mathbb{Z}_{2k})$ if and only if the row sums and column sums of A have the same parities.