On Lavoie's determinantal inequality

A determinantal inequality for positive semidefinite matrices

Let A,B,C be n× n positive semidefinite matrices. It is known that det(A+ B + C) + detC ≥ det(A+ C) + det(B + C), which includes det(A+B) ≥ detA+ detB as a special case. In this article, a relation between these two inequalities is proved, namely, det(A+ B + C) + detC − (det(A+ C) + det(B + C)) ≥ det(A+ B)− (detA+ detB).

On Some Quiver Determinantal Varieties

We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman’s complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when the complex resolves a maximal Cohen-Macaulay module supported on the quiver determinantal variety. This allows us to find the set-theoretical defining equat...

Notes on Determinantal Point Processes

In these notes we review the main concepts about Determinantal Point Processes. Determinantal point processes are of considerable current interest in Probability theory and Mathematical Physics. They were first introduced by Macchi ([8]) and they arise naturally in Random Matrix theory, non-intersecting paths, certain combinatorial and stochastic growth models and representation theory of large...

A Determinantal Inequality for the Geometric Mean with an Application in Diffusion Tensor Imaging

We prove that for positive semidefinite matrices A and B the eigenvalues of the geometric mean A#B are log-majorised by the eigenvalues of A1/2B1/2. From this follows the determinantal inequality det(I + A#B) ≤ det(I + A1/2B1/2). We then apply this inequality to the study of interpolation methods in diffusion tensor imaging.

Determinantal complexity