Abstract
We study a new class of matrices called diagonally magic matrices. We prove that such a matrix has rank at most 2 and that any square submatrix of a diagonally magic matrix is diagonally magic.
Highlights
1 Introduction For a positive integer n, let Sn be the set of all n! permutations of {, . . . , n}
We denote by Cn×n and Rn×n the set of n × n complex matrices and the set of n × n real matrices, respectively
A matrix A = ∈ Cn×n is called diagonally magic if n n ai,σ (i) = ai,π(i) for all σ, π ∈ Sn
Summary
For a positive integer n, let Sn be the set of all n! permutations of { , , . . . , n}. We will show that Bn and Cn are diagonally magic matrices. 2 Main results Let A = (ai,j) ∈ Cn×n be a diagonally magic matrix with n ≥ . From the definition of diagonally magic matrices ( ), we have a system of linear equations
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