5 papers
Linear Preservers of Infinitely Divisible Matrices
Shaun Fallat, Samir Mondal
An infinitely divisible nonnegative matrix is an entry-wise nonnegative matrix that admits an entry-wise nonnegative th root, with respect to usual matrix multiplication, for ev…
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…
Variations on Majorization of Vectors and Connections to Determinantal Inequalities
Shaun Fallat, Samir Mondal, Hristo Sendov
Majorization is a fundamental tool for comparing vectors, with connections to convexity, doubly stochastic matrices, eigenvalues, singular values, and zeros of polynomials. In matr…
Determinant Bounds for -Locally Positive Semidefinite Matrices
Shaun Fallat, Samir Mondal, Hristo Sendov
In this framework, the extremal case corresponds to the tightest nontrivial relaxation in this hierarchy, in which every proper principal submatrix is constrained to be positive se…
Linear Preservers of Real Matrix Classes Admitting a Real Logarithm
Shaun Fallat, Samir Mondal
In real Lie theory, matrices that admit a real logarithm reside in the identity component of the general linear group , wit…