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An Alternative Matrix Skew-Normal Random Matrix and Some Properties
Sankhya A, 2019The multivariate skew normal distribution has becoming increasingly popular, and is known to be flexible in real data fitting. In this paper, an alternative skew-normal random matrix, which is an extension of the multivariate skew-normal vector, is introduced.
Phil D. Young +3 more
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Exclusion and Inclusion Regions for the Eigenvalues of a Normal Matrix
SIAM Journal on Matrix Analysis and Applications, 2002Let \(A\) be an \(n\times n\) normal matrix with characteristic polynomial \(p(z)= f(x,y)+ ig(x,y)\). It is shown that because of the normality of \(A\), real analytic techniques yield bivariate polynomials such that generically, \[ \deg f\deg g\leq 4n\tag{1} \] holds pairwise, so that in the light of Bézout's theorem, (1) is of correct order.
Marko Huhtanen, Rasmus Munk Larsen
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Matrices Normal with Respect to an Hermitian Matrix
American Journal of Mathematics, 1938Verf. geht von der Bemerkung aus, daß \(A\) dann und nur dann im Schur-Toeplitzschen Sinne, normal (d. h. \(AA^* = A^*A\)) ist, wenn \(A^*\) eine Funktion (oder, da die Matrizen als endlich vorausgesetzt sind, ein Polynom) von \(A\) ist. Indem er die Einheitsmatrix \(E\) durch eine beliebige nichtsinguläre Hermitesche Matrix \(H\) ersetzt, definiert er
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On a bayes estimator of the matrix-normal density
Journal of Mathematical Sciences, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Closest normal matrix finally found!
BIT, 1987A method is given that will numerically find the closest normal matrix N (in the Frobenius norm) to a given matrix A by a sequence of unitary similarities. In the coordinate system of the eigenvectors of N, the obesity matrix of A is Hermitian. There is also a chapter with computed examples for the numerical ranges of N and A.
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Integral Equations and Operator Theory, 2000
The action of the group \(G_{lr}[m,n] \equiv GL(m,\mathbb{C}) \times GL(n,\mathbb{C})\) on the space of \(m \times n\) matrices over \(\mathbb{C}\) is classified and certain class of subgroups of \(G_{lr}[m,n]\) which are called admissible are introduced.
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The action of the group \(G_{lr}[m,n] \equiv GL(m,\mathbb{C}) \times GL(n,\mathbb{C})\) on the space of \(m \times n\) matrices over \(\mathbb{C}\) is classified and certain class of subgroups of \(G_{lr}[m,n]\) which are called admissible are introduced.
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An Estimator of Normal Covariance Matrix
Calcutta Statistical Association Bulletin, 1980Solliah (1964), by considering the group of lower triangular matrices, suggested an estimator of the normal covariance matrix Σ when the mean vector is known and the loss function is tr [Formula: see text] His estimator besides being minimax is better than the MLB of Σ.
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The extracellular matrix in normal and diseased myocardium
Journal of Nuclear Cardiology, 2001S, Hein, J, Schaper
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On the Jordan normal form of a matrix
AIP Conference Proceedings, 2023Elizaveta A. Kalinina, Elena A. Lezhnina
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The mle algorithm for the matrix normal distribution
Journal of Statistical Computation and Simulation, 1999Pierre Dutilleul
exaly