14 citations · 29 across the 17 of their papers we have counts for
17 papers
Consequences of Matrices Sharing Eigenvalues and Eigenvectors
Kayla Miller, Steven J. Miller, Fuzhen Zhang
While studying for a linear algebra final, the first named author prepared some test questions for herself to see how well she understood the material, and asked the second named a…
Comparison of the upper bounds for the extreme points of the polytopes of line-stochastic tensors
Fuzhen Zhang, Xiao-Dong Zhang
We call a real multi-dimensional array a {\em tensor} for short. In enumerating vertices of the polytopes of stochastic tensors, different approaches have been used: {(1)} Combinat…
Some matrix inequalities of log-majorization type
Bo-Yan Xi, Fuzhen Zhang
The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to general…
Enumerating extreme points of the polytopes of stochastic tensors: an optimization approac
Fuzhen Zhang, Xiao-Dong Zhang
This paper is concerned with the extreme points of the polytopes of stochastic tensors. By a tensor we mean a multi-dimensional array over the real number field. A line-stochastic…
Eigenvalue continuity and Geršgorin's theorem
Chi-Kwong Li, Fuzhen Zhang
Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly.…
Harnack type inequalities for matrices in majorization
Chaojun Yang, Fuzhen Zhang
Following the recent work of Jiang and Lin (Linear Algebra Appl. 585 (2020) 45--49), we present more results (bounds) on Harnack type inequalities for matrices in terms of majoriza…
Inequalities for selected eigenvalues of the product of matrices
Bo-Yan Xi, Fuzhen Zhang
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.
The permanent functions of tensors
Qing-Wen Wang, Fuzhen Zhang
By a tensor we mean a multidimensional array (matrix) or hypermatrix over a number field. This article aims to set an account of the studies on the permanent functions of tensors.…
On the number of vertices of the stochastic tensor polytope
Zhongshan Li, Fuzhen Zhang, Xiao-Dong Zhang
This paper is devoted to the study of lower and upper bounds for the number of vertices of the polytope of stochastic tensors (i.e., triply stochastic arrays of…
An extension of Harnack type determinantal inequality
Minghua Lin, Fuzhen Zhang
We revisit and comment on the Harnack type determinantal inequality for contractive matrices obtained by Tung in the nineteen sixtieth and give an extension of the inequality invol…
Polytopes of Stochastic Tensors
Haixia Chang, Vehbi E. Paksoy, Fuzhen Zhang
Considering stochastic tensors (i.e., nonnegative hypermatrices in which every sum over one index , , or , is 1), we study the polytope ($Ω…
An update on a few permanent conjectures
Fuzhen Zhang
We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top…
An inequality for tensor product of positive operators and its applications
Xaixia Chang, Vehbi E. Paksoy, Fuzhen Zhang
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of let…
Book Review: Matrix Theory by X. Zhan
Fuzhen Zhang
This is a book review for Zhan's Matrix Theory (AMS, GSM 147, 2013).
Positivity of Partitioned Hermitian Matrices with Unitarily Invariant Norms
Chi-Kwong Li, Fuzhen Zhang
We give a short proof of a recent result of Drury on the positivity of a matrix of the form for any rectangular complex (or…
Angles, triangle inequalities, correlation matrices and metric-preserving and subadditive functions
Diego Castano, Vehbi E. Paksoy, Fuzhen Zhang
We study the triangle inequalities for angles (with different definitions) and present inequalities concerning the entries of correlation matrices through the positivity of $3\time…
An operator equality involving a continuous field of operators and its norm inequalities
Mohammad Sal Moslehian, Fuzhen Zhang
Let be a -algebra, be a locally compact Hausdorff space equipped with a probability measure and let be a continuous field of operators…