Results 1 to 10 of about 221 (44)

Equalities for orthogonal projectors and their operations

Open Mathematics, 2010
Tian Yongge
doaj   +1 more source

Inertias and ranks of some Hermitian matrix functions with applications

Open Mathematics, 2012
Zhang Xiang, Wang Qing-Wen, Liu Xin
doaj   +1 more source

Solutions of the matrix inequalities in the minus partial ordering and Löwner partial ordering

, 2013
Yongge Tian
semanticscholar   +1 more source

Circulant Hadamard matrices and Hermitian circulant complex Hadamard matrices

, 2021
We prove that there exists a circulant Hadamard matrix of order n if and only if there exists a Hermitian circulant complex Hadamard matrix of order n and that there does not exist a Butson-type Hermitian circulant complex Hadamard matrix of order n > 4.
Norichika Matsuki
semanticscholar   +1 more source

Equality in Wielandt’s eigenvalue inequality

Special Matrices, 2015
In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.
Friedland Shmuel
doaj   +4 more sources

Graph complement conjecture for classes of shadow graphs

Operators and Matrices, 2021
The real minimum semidefinite rank of a graph G , denoted mrR+(G) , is defined to be the minimum rank among all real symmetric positive semidefinite matrices whose zero/nonzero pattern corresponds to the graph G .
Monsikarn Jansrang, S. Narayan
semanticscholar   +1 more source

A note on two-sided removal and cancellation properties associated with Hermitian matrix

, 2021
A complex square matrix A is said to be Hermitian if A = A∗, the conjugate transpose of A. We prove that each of the two triple matrix product equalities AA∗A = A∗AA∗ and A3 = AA∗A implies that A is Hermitian by means of decompositions and determinants
Yongge Tian
semanticscholar   +1 more source

Cospectral constructions for several graph matrices using cousin vertices

Special Matrices, 2021
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum.
Lorenzen Kate
doaj   +1 more source

Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields

Special Matrices, 2021
The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽n×n is defined as ℓ1ℓ2· · · ℓn, where ℓj ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero ...
Dukes Peter J., Martínez-Rivera Xavier
doaj   +1 more source

The complete positivity of symmetric tridiagonal and pentadiagonal matrices

Special Matrices, 2022
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix AA is completely positive. Our decomposition can be applied to a wide range of matrices.
Cao Lei, McLaren Darian, Plosker Sarah
doaj   +1 more source