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On positive definite solution of nonlinear matrix equations

Linear and Multilinear Algebra, 2017
AbstractIn this article, we present a sufficient condition for the existence of a unique positive definite solution of the non-linear matrix equation , where , (the set of all Hermitian positive definite matrices), are non-singular matrices and are order-preserving mappings. We give an example of a non-linear matrix equation of the above form (, A is a
Sk. Monowar Hossein   +2 more
openaire   +1 more source

Positive definite solution of a nonlinear matrix equation

Journal of Fixed Point Theory and Applications, 2016
The authors use fixed-point theory to present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation \(X=Q\pm\sum_{i1}^m A_i^* F(X)A_i\), where \(Q\) is a positive definite matrix, \(A_i\)'s are arbitrary \(n\times n\) matrices and \(F\) is a monotone map from the set of positive definite matrices to ...
Bose, Snehasish   +2 more
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The approximate factorization of positive-definite matrix functions

Russian Mathematical Surveys, 1999
It is well known that the prediction problem for a stationary process can be reduced to that of factorizing a positive-definite matrix function \(S(t)\) as \(S(t)= \chi^+(t)\cdot(\chi^+(t))^*\), \(|t|= 1\), where \(\chi^+\) is an outer analytic matrix function with entries of Hardy class \(H_2\) and \(^*\) denotes the Hermitian conjugate.
Janashia, G. A.   +2 more
openaire   +2 more sources

A positive-definite matrix which is not extendible

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1984
This note treats the problem of extendibility of a positive-definite matrix. The difference between extendibility and positive- semidefiniteness in multiple dimensions is described. The construction of a positive definite nonextendible correlation matrix is also given.
openaire   +2 more sources

Image clustering based on hermetian positive definite matrix and radial Jacobi moments

International Symposium on Computer Vision, 2018
A. Hjouji   +4 more
semanticscholar   +1 more source

The biofilm matrix: multitasking in a shared space

Nature Reviews Microbiology, 2022
Hans-Curt Flemming   +2 more
exaly  

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