Type II Matrices of Size Five

Abstract

. A type II matrix is an n×n matrix W with non-zero entries W _i,j which satisfies , i, j=1, …, n. Two type II matrices W, W′ are said to be equivalent if W′=P ₁Δ₁ WΔ₂ P ₂ holds for some permutation matrices P ₁, P ₂ and for some non-singular diagonal matrices Δ₁, Δ₂. In the present paper, it is shown that there are up to equivalence exactly three type II matrices in M ₅(C).