Results 11 to 20 of about 40 (30)
Trace inequalities for positive semidefinite matrices
Discussiones Mathematicae - General Algebra and Applications, 2017 Certain trace inequalities for positive definite matrices are generalized for positive semidefinite matrices using the notion of the group generalized inverse.
Choudhury Projesh Nath, Sivakumar K.C.
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On relationships between two linear subspaces and two orthogonal projectors
Special Matrices, 2019 Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their ...
Tian Yongge
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Special Matrices, 2017 We take as given a real symmetric matrix A, whose graph is a tree T, and the eigenvalues of A, with their multiplicities. Each edge of T may then be classified in one of four categories, based upon the change in multiplicity of a particular eigenvalue ...
Toyonaga Kenji, Johnson Charles R.
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On some classical trace inequalities and a new Hilbert-Schmidt norm inequality
, 2018 Let A be a positive semidefinite matrix and B be a Hermitian matrix. Using some classical trace inequalities, we prove, among other inequalities, that ∥ ∥AsB+BA1−s ∥ ∥ 2 ∥ ∥AtB+BA1−t ∥ ∥ 2 for 2 s t 1 . We conjecture that this inequality is also true for
M. Hayajneh, Saja Hayajneh, F. Kittaneh
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A canonical form for H-unitary matrices
, 2016 In this paper matrices A are considered that have the property that A∗HA = H , where H = H∗ is invertible. A canonical form is given for the pair of matrices (A,H) under transformations (A,H) → (S−1AS,S∗HS) , where S is invertible, in which the canonical
G. Groenewald, D. V. Rensburg, A. Ran
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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
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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
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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
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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
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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
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