On Standard Forms of the Pairs of Matrices Over the Ring of Gaussian Integers with Respect to the (z,k)-Equivalence
摘要
We study the (z,k)-equivalence of the pairs of matrices over the ring of Gaussian integers and their reducibility to standard forms. It is shown that the number of standard forms of the pairs of matrices over this ring is finite. The classes of the pairs of matrices with minimum and maximum numbers of standard forms are presented.