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Two absolutely bounded determinantal ratios
Hristo Sendov, Mengxu Yuan
Bounded ratios of products of minors of positive definite matrices have a long history, starting with Hadamard's inequality in 1893. It states that for every positive semidefinite…
A Bounded Determinantal Ratio for Positive Definite Matrices
Hristo Sendov
Bounded ratios between products of minors of a positive definite matrix have a long history. Starting with Hadamard's inequality which bounds from above the determinant by the prod…
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…
Aggregate Bounds on the eigenvalues of the principal submatrices of a Hermitian matrix and majorization relations
Hristo Sendov, Mengxu Yuan
We extend bounds, proved by R.C. Thompson in 1966, on the sum of the -th largest eigenvalues of the principal matrices of an Hermitian matrix.…