Results 21 to 30 of about 222 (44)
PRESERVERS OF MATRIX PAIRS WITH A FIXED INNER PRODUCT VALUE
, 2012 Let V be the set of n×n hermitian matrices, the set of n×n symmetric matrices, the set of all effects, or the set of all projections of rank one. Let c be a real number. We characterize bijective maps φ : V → V satisfying tr (AB) = c ⇐⇒ tr (φ(A)φ(B)) = c
Chi-Kwong Li, Lucijan Plevnik, P. Šemrl
semanticscholar +1 more source
A simple sufficient condition for complete positivity
, 2015 We use row sums and rank to give a sufficient condition on the diagonal entries of a doubly nonnegative matrix for it to be completely positive and its cp-rank equal to its rank. Mathematics subject classification (2010): 15A23, 15B48, 15B57.
W. So, Changqing Xu
semanticscholar +1 more source
A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric [PDF]
, 2017 We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic perspective.
Zimmermann, Ralf
core +2 more sources
Orthonormal Jordan bases in finite dimensional Hilbert spaces
, 2015 Necessary and sufficient conditions are presented for a linear operator in a finite dimensional complex or real Hilbert space to have a Jordan form in an orthonormal basis. Further, necessary conditions are given in terms of the self-commutator operator.
B. Nagy
semanticscholar +1 more source
Concrete minimal 3 × 3 Hermitian matrices and some general cases
Demonstratio Mathematica, 2017 Given a Hermitian matrix M ∈ M3(ℂ) we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm.
Klobouk Abel H., Varela Alejandro
doaj +1 more source
Nonnegative definite hermitian matrices with increasing principal minors
, 2013 A nonzero nonnegative definite hermitian m by m matrix A has increasing principal minors if the value of each principle minor of A is not less than the value each of its subminors. For $m>1$ we show $A$ has increasing principal minors if and only if $A^{-
Friedland, Shmuel
core +1 more source
Sufficient conditions for complete positivity
, 2011 Marcus and Minc gave sufficient conditions on the diagonal entries of a doubly nonnegative doubly stochastic n×n matrix A , that there is a doubly nonnegative doubly stochastic matrix C with A = C2 . In this event, A is completely positive.
Robert Reams
semanticscholar +1 more source
On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs
, 2015 The principal permanent rank characteristic sequence is a binary sequence $r_0 r_1 \ldots r_n$ where $r_k = 1$ if there exists a principal square submatrix of size $k$ with nonzero permanent and $r_k = 0$ otherwise, and $r_0 = 1$ if there is a zero ...
Horn, Paul +5 more
core +1 more source
Linear preservers and quantum information science
, 2012 Let $m,n\ge 2$ be positive integers, $M_m$ the set of $m\times m$ complex matrices and $M_n$ the set of $n\times n$ complex matrices. Regard $M_{mn}$ as the tensor space $M_m\otimes M_n$. Suppose $|\cdot|$ is the Ky Fan $k$-norm with $1 \le k \le mn$, or
Fosner, Ajda +3 more
core +1 more source
Existence of a Not Necessarily Symmetric Matrix with Given Distinct Eigenvalues and Graph
, 2016 For given k distinct complex conjugate pairs, l distinct real numbers, and a given graph G on 2k+l vertices with a matching of size at least k, we will show that there is a real matrix whose eigenvalues are the given numbers and its graph is G.
Monfared, Keivan Hassani
core +1 more source