[PDF][PDF] Hadamard, Khatri-Rao, Kronecker and other matrix products

S Liu, G Trenkler - … Journal of Information and Systems Sciences, 2008 - academia.edu
Matrices and matrix operations are studied and applied in many areas such as engineering,
natural and social sciences. Books written on these topics include Berman et al.(1989) …

[HTML][HTML] Some new connections between matrix products for partitioned and non-partitioned matrices

Z Al Zhour, A Kiliçman - Computers & Mathematics with Applications, 2007 - Elsevier
This paper is concerned with a long list of matrix products for partitioned and non-partitioned
matrices, including Kronecker, Khatri–Rao of first kind, Hadamard, Tracy–Singh, Khatri–Rao …

[HTML][HTML] Vector least-squares solutions for coupled singular matrix equations

A Kılıçman, ZAA Al Zhour - Journal of Computational and Applied …, 2007 - Elsevier
The weighted least-squares solutions of coupled singular matrix equations are too difficult to
obtain by applying matrices decomposition. In this paper, a family of algorithms are applied …

[HTML][HTML] New techniques for solving some matrix and matrix differential equations

ZAA Al-Zhour - Ain Shams Engineering Journal, 2015 - Elsevier
Matrix and matrix differential equations play an important role in system theory, control
theory, stability theory of differential equations, communication systems and many other …

[HTML][HTML] Efficient solutions of coupled matrix and matrix differential equations

Z Al-Zhour - 2012 - scirp.org
In Kronecker products works, matrices are sometimes regarded as vectors and vectors are
sometimes made in to matrices. To be precise about these reshaping we use the vector and …

[HTML][HTML] The general solutions of singular and non-singular matrix fractional time-varying descriptor systems with constant coefficient matrices in Caputo sense

Z Al-Zhour - Alexandria engineering journal, 2016 - Elsevier
In this paper, we generalize the time-varying descriptor systems to the case of fractional
order in matrix forms. Moreover, we present the general exact solutions of the linear singular …

RETRACTED: The general (vector) solutions of such linear (coupled) matrix fractional differential equations by using Kronecker structures

ZAA Al-Zhour - 2014 - Elsevier
After receiving a report from a reader, the Editor-in-Chief consulted a third party expert and
an Associate Editor of the journal. The response from the author has been considered …

Model reduction of quadratic-bilinear descriptor systems via Carleman bilinearization

P Goyal, MI Ahmad, P Benner - 2015 European Control …, 2015 - ieeexplore.ieee.org
We propose a model reduction technique for quadratic-bilinear descriptor systems. The
approach involves approximating the system by a bilinear descriptor system using Carleman …

[PDF][PDF] k-fractional integral inequalities of Hadamard type for exponentially (s, m)-convex functions

AU Rehman, G Farid, S Bibi, CY Jung, SM Kang - AIMS Math, 2021 - aimspress.com
The aim of this article is to present fractional versions of the Hadamard type inequalities for
exponentially (s, m)-convex functions via k-analogue of Riemann-Liouville fractional …

[PDF][PDF] New representations for weighted Drazin inverse of matrices

Z Al-Zhour, A Kılıçman, MHA Hassa - International Journal of …, 2007 - academia.edu
In this paper, the result are established in the following four ways: First, we present a general
representation for the weighted Drazin inverse Ad, W of an arbitrary rectangular matrix A∈ …