Strict Sign-Central Matrices

Tight sign-central matrices

A real matrix A is called sign-central if the convex hull of the columns of à contains the zero vector 0 for every matrix à with the same sign pattern as A. A sign-central matrix A is called a minimal sign-central matrix if the deletion of any of the columns of A breaks the signcentrality of A. A sign-central matrix A is called tight sign-central if the Hadamard (entrywise) product of any two c...

A stable test for strict sign regularity

A stable test to check if a given matrix is strictly sign regular is provided. Among other nice properties, we prove that it has an optimal growth factor. The test is compared with other alternative tests appearing in the literature, and its advantages are shown.

Alternating sign matrices

Symmetric alternating sign matrices

In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can ...

Affine Alternating Sign Matrices

An Alternating sign matrix is a square matrix of 0’s, 1’s, and −1’s in which the sum of the entries in each row or column is 1 and the signs of the nonzero entries in each row or column alternate. This paper attempts to define an analogue to alternating sign matrices which is infinite and periodic. After showing the analogue we define shares desirable cahracteristics with alternating sign matri...