A Complete System of Invariants with Respect to Similarity for Pairs of Matrices of Even Order with Characteristic Matrix of Special Smith form

We study the similarity of a pair of matrices of even order with special Smith form and certain conditions for the decomposability of the characteristic matrix of the pair. In this connection, we obtain a complete system of invariants for this class of pairs of matrices with respect to similarity. The results obtained are stated in the classical terms of ranks, of minimal indices, and of elementary divisors of matrices (both finite and infinite).