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Functions Operating on Positive Semidefinite Quaternionic Matrices

open access: yesMonatshefte Fur Mathematik, 2001
We study functions phi : B --> H on the quaternionic unit ball B := {z is an element of H : /z/ less than or equal to 1} which operate on positive semidefinite matrices in the sense that (phi (a(ij))) is positive semidefinite whenever (a(ij)) is a ...
Helge Glöckner
exaly   +2 more sources

Approximation by a Hermitian Positive Semidefinite Toeplitz Matrix

SIAM Journal on Matrix Analysis and Applications, 1993
The authors study the problem of finding the closest Hermitian positive semidefinite Toeplitz matrix of a given rank to an arbitrary given matrix (in the Frobenius norm = Hilbert-Schmidt norm). They introduce two methods, one is based on using a special orthonormal basis in the space of Hermitian Toeplitz matrices and the second is a modified ...
T. J. Suffridge, Tom L. Hayden
openaire   +2 more sources

Cholesky decomposition of a positive semidefinite matrix with known kernel

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zdenek Dostál   +3 more
openaire   +1 more source

A note on Hermitian positive semidefinite matrix polynomials

Linear Algebra and its Applications, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Friedland, A. Melman
openaire   +1 more source

The Probability that a (partial) matrix is positive semidefinite

1998
Assuming that a ij is distributed uniformly in [—1,1] and a ii = 1, we compute the probability that a symmetric matrix A = [a ij ] 171-1 j=1 is positive semidefinite. The probability is also computed if A is a Toeplitz matrix. Finally, some results for partial matrices are presented.
C. R. Johnson, G. Nævdal
openaire   +1 more source

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