Results 11 to 20 of about 1,468 (179)
An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices
Special Matrices, 2021 A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.
Hutchinson George
doaj +1 more source
Analysis of Fixing Nodes Used in Generalized Inverse Computation
Advances in Electrical and Electronic Engineering, 2014 In various fields of numerical mathematics, there arises the need to compute a generalized inverse of a symmetric positive semidefinite matrix, for example in the solution of contact problems.
Pavla Hruskova
doaj +1 more source
Positive Semidefinite Matrices, Exponential Convexity for Majorization, and Related Cauchy Means
Journal of Inequalities and Applications, 2010 We prove positive semidefiniteness of matrices generated by differences deduced from majorization-type results which implies exponential convexity and log-convexity of these differences and also obtain Lyapunov's and Dresher's inequalities for ...
N. Latif +2 more
doaj +2 more sources
Poisson Quantum Information [PDF]
Quantum, 2021 By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information.
Mankei Tsang
doaj +1 more source
A New Algorithm for Positive Semidefinite Matrix Completion
Journal of Applied Mathematics, 2016 Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and low-rank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control.
Fangfang Xu, Peng Pan
doaj +1 more source
A counterexample to the Drury permanent conjecture
Special Matrices, 2017 We offer a counterexample to a conjecture concerning the permanent of positive semidefinite matrices. The counterexample is a 4 × 4 complex correlation matrix.
Hutchinson George
doaj +1 more source
Hilbert’s 17th problem in free skew fields
Forum of Mathematics, Sigma, 2020 This paper solves the rational noncommutative analogue of Hilbert’s 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of Hermitian matrices in its domain, then it is a sum of Hermitian squares of noncommutative ...
Jurij Volčič
doaj +1 more source
A Characterization on Singular Value Inequalities of Matrices
Journal of Function Spaces, 2020 We obtain a characterization of pair matrices A and B of order n such that sjA≤sjB, j=1, …, n, where sjX denotes the j-th largest singular values of X. It can imply not only some well-known singular value inequalities for sums and direct sums of matrices
Wei Dai, Yongsheng Ye
doaj +1 more source
有关矩阵广义逆的惯性指数及其应用(Inertia formulae related to the generalized inverse with applications)
Zhejiang Daxue xuebao. Lixue ban, 2019 In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse . Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices.
WUZhongcheng(吴中成) +1 more
doaj +1 more source
The resolvent average for positive semidefinite matrices
Linear Algebra and its Applications, 2010 We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean.
Bauschke, Heinz H. +2 more
openaire +3 more sources