Inverse Eigenvalue Problem and Least-Squares Problem for Skew-Hermitian {P,K + 1}-Reflexive Matrices
Journal of Mathematics, 2022 This paper involves related inverse eigenvalue problem and least-squares problem of skew-Hermitian {P,k + 1}-reflexive(antireflexive) matrices and their optimal approximation problems.
Chang-Zhou Dong, Hao-Xue Li
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Pfaffian Expressions for Random Matrix Correlation Functions [PDF]
, 2007 It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of ...
T. Nagao
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A flexible short recurrence Krylov subspace method for matrices arising in the time integration of port-Hamiltonian systems and ODEs/DAEs with a dissipative Hamiltonian [PDF]
BIT Numerical Mathematics, 2022 For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model.
M. Diab, A. Frommer, K. Kahl
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Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices [PDF]
Studies in applied mathematics (Cambridge), 2022 We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix.
A. Iserles, M. Webb
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High-Order Retractions on Matrix Manifolds Using Projected Polynomials [PDF]
SIAM Journal on Matrix Analysis and Applications, 2017 We derive a family of high-order, structure-preserving approximations of the Riemannian exponential map on several matrix manifolds, including the group of unitary matrices, the Grassmannian manifold, and the Stiefel manifold.
Evan S. Gawlik, M. Leok
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Real dimension of the Lie algebra of S-skew-Hermitian matrices
The Electronic Journal of Linear Algebra, 2022 Let $M_n(\mathbb{C})$ be the set of $n\times n$ matrices over the complex numbers. Let $S \in M_n(\mathbb{C})$. A matrix $A\in M_n(\mathbb{C})$ is said to be $S$-skew-Hermitian if $SA^*=-AS$ where $A^*$ is the conjugate transpose of $A$.
Jonathan Caalim, Yuuji Tanaka
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Averages over Ginibre's Ensemble of Random Real Matrices [PDF]
, 2006 We give a method for computing the ensemble average of multiplicative class func-tions over the Gaussian ensemble of real asymmetric matrices. These averages areexpressed in terms of the Pfaffian of Gram-like antisymmetric matrices formed withrespect to a ...
C. Sinclair
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Symmetry, 2021 In this article, we study the solvability conditions and the general solution of a system of matrix equations involving η-skew-Hermitian quaternion matrices.
A. Rehman +3 more
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Several matrix trace inequalities on Hermitian and skew-Hermitian matrices
Journal of Inequalities and Applications, 2014 In this paper, we present several matrix trace inequalities on Hermitian and skew-Hermitian matrices, which play an important role in designing and analyzing interior-point methods (IPMs) for semidefinite optimization (SDO).
Xiangyu Gao +3 more
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Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings [PDF]
, 2002 We equip the complex polynomial algebra C[t] with the involution which is the identity on C and sends t to -t. Answering a question raised by V.G. Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to the direct sum
D. Djoković, F. Szechtman
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