AbstractLet X, Y be two normal n × n matrices over C with respective spectra x1,…, xn and y>1,…, yn. Marcus and de Oliveira conjectured that the determinant of X + Y lies in the convex hull generated by the n! complex points Πni=1(xi + y)σ(i)), where σ ranges over the symmetric group Sn. We prove the conjecture for the case that n−2 of the yi are equal. First the problem is reduced to the question of nonnegative solvability of a certain system of linear equations. Then the required nonnegative solvability is demonstrated by involving a measure theoretic generalization of the marriage lemma. Our main result forms a positive counterpart to a recent example given by Drury
AbstractSome parts of an earlier paper by the authors are revised and further developed
AbstractLet A be an n × n normal matrix, and let 1 ⪕ m < n. Let α,β ϵ Qm,n, the set of increasing in...
AbstractIt is shown that the determinant of the sum of a positive definite hermitian matrix and a sk...
AbstractThe first part of this paper presents an approach to a possible salvation of an idea advance...
AbstractLet X,Y be matrices of spectra x1,…,xn and y1,…,yn, respectively. For a wide class of pairs ...
AbstractLet Un be the group of the unitary n×n matrices. Let A=diag(α1,…,αn), B=diag(β1,…,βn), where...
AbstractWe provide a theorem and a counterexample relating to the determinantal conjecture of Marcus...
AbstractWe establish the following case of the Determinantal Conjecture of Marcus [M. Marcus, Deriva...
AbstractLet A, B, U ∈ ℂ n x n, A = diag(aj), B = diag(bj), U unitary, D=det(A+UBUH),zσ=∏j=1n(aj+bσ(...
The well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determinant det...
AbstractLet A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of dete...
Let A, B, C be n × n positive semidefinite matrices. It is known that det(A + B + C) + det C ≥ det(A...
We view the well known determinantal conjecture of de Oliveira and Marcus as a special case of an as...
AbstractSuppose m and n are integers such that 1⩽m⩽n, and H is a subgroup of the symmetric group Sm ...
AbstractQueiró and Kovačec have recently established an inequality for the modulus of the determinan...
AbstractSome parts of an earlier paper by the authors are revised and further developed
AbstractLet A be an n × n normal matrix, and let 1 ⪕ m < n. Let α,β ϵ Qm,n, the set of increasing in...
AbstractIt is shown that the determinant of the sum of a positive definite hermitian matrix and a sk...
AbstractThe first part of this paper presents an approach to a possible salvation of an idea advance...
AbstractLet X,Y be matrices of spectra x1,…,xn and y1,…,yn, respectively. For a wide class of pairs ...
AbstractLet Un be the group of the unitary n×n matrices. Let A=diag(α1,…,αn), B=diag(β1,…,βn), where...
AbstractWe provide a theorem and a counterexample relating to the determinantal conjecture of Marcus...
AbstractWe establish the following case of the Determinantal Conjecture of Marcus [M. Marcus, Deriva...
AbstractLet A, B, U ∈ ℂ n x n, A = diag(aj), B = diag(bj), U unitary, D=det(A+UBUH),zσ=∏j=1n(aj+bσ(...
The well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determinant det...
AbstractLet A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of dete...
Let A, B, C be n × n positive semidefinite matrices. It is known that det(A + B + C) + det C ≥ det(A...
We view the well known determinantal conjecture of de Oliveira and Marcus as a special case of an as...
AbstractSuppose m and n are integers such that 1⩽m⩽n, and H is a subgroup of the symmetric group Sm ...
AbstractQueiró and Kovačec have recently established an inequality for the modulus of the determinan...
AbstractSome parts of an earlier paper by the authors are revised and further developed
AbstractLet A be an n × n normal matrix, and let 1 ⪕ m < n. Let α,β ϵ Qm,n, the set of increasing in...
AbstractIt is shown that the determinant of the sum of a positive definite hermitian matrix and a sk...