Results 11 to 20 of about 222 (44)
On the spectral properties of a class of $H$-selfadjoint random matrices and the underlying combinatorics [PDF]
, 2013 An expansion of the Weyl function of a $H$-selfadjoint random matrix with one negative square is provided. It is shown that the coefficients converge to a certain generalization of Catlan numbers.
Pagacz, Patryk, Wojtylak, Michal
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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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Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue
Special Matrices, 2020 Let A = [aij] be a real symmetric matrix. If f : (0, ∞) → [0, ∞) is a Bernstein function, a sufficient condition for the matrix [f (aij)] to have only one positive eigenvalue is presented.
Al-Saafin Doaa, Garloff Jürgen
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The inertia of the symmetric approximation for low-rank matrices [PDF]
, 2017 © 2017 Informa UK Limited, trading as Taylor & Francis Group In many areas of applied linear algebra, it is necessary to work with matrix approximations.
Casanellas Rius, Marta +2 more
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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. Kıttaneh
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Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions [PDF]
, 2017 Fractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement.
Hogben, L +3 more
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A constructive arbitrary-degree Kronecker product decomposition of tensors [PDF]
, 2016 We propose the tensor Kronecker product singular value decomposition~(TKPSVD) that decomposes a real $k$-way tensor $\mathcal{A}$ into a linear combination of tensor Kronecker products with an arbitrary number of $d$ factors $\mathcal{A} = \sum_{j=1}^R ...
Batselier, Kim, Wong, Ngai
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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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