Inverses and eigenvalues of diamondalternating sign matrices

Abstract

An n × n diamond alternating sign matrix (ASM) is a (0, +1, −1)-matrix with ±1 entries alternatingand arranged in a diamond-shaped pattern. The explicit inverse (for n even) or generalized inverse (for nodd) of a diamond ASM is derived. The eigenvalues of diamond ASMs are considered and when n is even, thecharacteristic polynomial, which involves signed binomial coefficients, is determined.

Keywords

• diamond alternating sign matrix
• inverse
• generalized inverse
• eigenvalue
• binomial coefficients
• 15a09
• 15a18
• 15b36