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The determinant of the distance matrix of graphs with blocks at most bicyclic
(Elsevier Science Inc., 2021-04-01)
Let G be a connected graph on n vertices and D(G) be its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known when the graph is either a tree or a unicyclic ...
Spectral shorted matrices
(Elsevier Science Inc, 2004-04)
Given a n x n positive semidefinite matrix A and a subspace S of C^n, Σ (S, A) denotes the shorted matrix of A to S. We consider the notion of spectral shorted matrix φ(S, A) = lim _{m→∞} Σ (S, A^m )^{1/m}. We completely ...
On the spectral radius of block graphs with prescribed independence number α
(Elsevier, 2021-04)
Let G(n,α) be the class of block graphs on n vertices and prescribed independence number α. In this article we prove that the maximum spectral radius ρ(G), among all graphs G∈G(n,α), is reached at a unique graph. As a ...
Schur complements of selfadjoint Krein space operators
(Elsevier Science Inc, 2019-11)
Given a bounded selfadjoint operator W on a Krein space H and a closed subspace S of H, the Schur complement of W to S is defined under the hypothesis of weak complementability. A variational characterization of the Schur ...
Generalized Schur complements and P-complementable operators
(Elsevier Science Inc, 2004-12)
Let A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space H. We say that A is P-complementable if A−µP≥ 0 holds for some µ ∈ R. In this case we define IP (A) = max{µ ∈ R : A − µP ...
Local extrema for Procrustes problems in the set of positive definite matrices
(Elsevier Science Inc, 2020-05)
Given two positive definite matrices A and B, a well known result by Gelfand, Naimark and Lidskii establishes a relationship between the eigenvalues of A and B and those of AB by means of majorization inequalities. In this ...
Local Lidskii's theorems for unitarily invariant norms
(Elsevier Science Inc, 2018-11)
Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpreted as an explicit description of global minimizers of functions that are built on unitarily invariant norms, with domains consisting ...
Shorting selfadjoint operators in Hilbert spaces
(Elsevier Science Inc, 2008-04)
Given a closed subspace S of a Hilbert space H and a (bounded) selfadjoint operator B acting on H, a min-max representation of the shorted operator (or Schur complement) of B to S is obtained under compatibility hypotheses. ...
Characterizations of k-commutative equalities for some outer generalized inverses
(Taylor & Francis Ltd, 2018-07)
In this paper, we present necessary and sufficient conditions for the k-commutative equality $A^k X = X A^k$, where $X$ is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, ...
On Rosenhein-Göpel configurations and integrable systems
(SP MAIK Nauka/Interperiodica, 2011)