Results 41 to 50 of about 3,570,033 (364)
Unitary equivalence to a complex symmetric matrix: a modulus criterion [PDF]
, 2010 We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods.
S. Garcia, Daniel E. Poore, M. Wyse
semanticscholar +1 more source
Symmetric multisplitting of a symmetric positive definite matrix
Linear Algebra and its Applications, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhi-Hao Cao, Zhong-Yun Liu
openaire +2 more sources
PT Symmetry as a Generalization of Hermiticity
, 2010 The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases.
Ballentine L E +9 more
core +1 more source
Cauchy's interlace theorem and lower bounds for the spectral radius
International Journal of Mathematics and Mathematical Sciences, 2000 We present a short and simple proof of the well-known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.
A. McD. Mercer, Peter R. Mercer
doaj +1 more source
Smoothed analysis of symmetric random matrices with continuous distributions [PDF]
, 2015 We study invertibility of matrices of the form $D+R$ where $D$ is an arbitrary symmetric deterministic matrix, and $R$ is a symmetric random matrix whose independent entries have continuous distributions with bounded densities. We show that $|(D+R)^{-1}|
Farrell, Brendan, Vershynin, Roman
core +3 more sources
The derivative of an orthogonal matrix of eigenvectors of a symmetric matrix
Linear Algebra and its Applications, 1997 Let \(M\) be a real symmetric \(p\times p\) matrix with distinct eigenvalues \(\lambda_i\) and associated normalized eigenvectors \(w_i\), \(1\leq i\leq p\). There are real-valued functions \(\psi_i\) and vector-valued functions \(f_i\) defined for all matrices \(Z\) in some neighborhood \({\mathcal N} (M) \subseteq \mathbb{R}^{p \times p}\) of \(M ...
Kollo, T., Neudecker, H.
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Symmetrical parametrizations of the lepton mixing matrix [PDF]
Physical Review D, 2011 Advantages of the original symmetrical form of the parametrization of the lepton mixing matrix are discussed. It provides a conceptually more transparent description of neutrino oscillations and lepton number violating processes like neutrinoless double beta decay, clarifying the significance of Dirac and Majorana phases.
Rodejohann, Werner +1 more
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PT-Symmetric, Quasi-Exactly Solvable matrix Hamiltonians [PDF]
, 2007 Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces.
Ancilla Nininahazwe +8 more
core +2 more sources
Unitary equivalence to a complex symmetric matrix: geometric criteria [PDF]
, 2009 We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix.
S. Garcia, L. Balayan
semanticscholar +1 more source
Journal of Computational and Applied Mathematics, 1991 Typical matrix eigenvalue problems, quadratic or linear, are best formulated as pencils \((A,M)\) in which both \(A\) and \(M\) are real and symmetric. This fact is emphasized in the paper through a set of physical examples. Then, the canonical forms are used to explain the role of the sign characteristic attached to real eigenvalues.
openaire +3 more sources