20 citations · 22 across the 7 of their papers we have counts for
7 papers
Powers, Roots, and Positivity
Charles R Johnson, Samir Mondal, Michael J. Tsatsomeros
There is a remarkable variety of natural generalizations of the notion of scalar positivity to square matrices. The lists and tables indicate those that we consider here; they are…
How to Detect and Construct N-matrices
Projesh Nath Choudhury, Michael J. Tsatsomeros
N-matrices are real matrices all of whose principal minors are negative. We provide (i) an test to detect whether or not a given matrix is an N-matrix, and (ii…
Inverse Relations in Shapiro's Open Questions
Ik-Pyo Kim, Michael J. Tsatsomeros
As an inverse relation, involution with an invariant sequence plays a key role in combinatorics and features prominently in some of Shapiro's open questions [L.W. Shapiro, Some ope…
Pascal Eigenspaces and Invariant Sequences of the First or Second Kind
Ik-Pyo Kim, Michael J. Tsatsomeros
An infinite real sequence is called an invariant sequence of the first (resp., second) kind if (resp., $a_n=\sum_{k=n}^{\infty…
Matrix Roots of Eventually Positive Matrices
Judith J. McDonald, Pietro Paparella, Michael J. Tsatsomeros
Eventually positive matrices are real matrices whose powers become and remain strictly positive. As such, eventually positive matrices are a fortiori matrix roots of positive matri…
Principal pivot transforms: properties and applications
Michael Tsatsomeros
The principal pivot transform (PPT) of a matrix A partitioned relative to an invertible leading principal submatrix is a matrix B such that A [x_1^T x_2^T]^T = [y_1^T y_2^T]^T if a…