[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] The representation and approximation for the weighted Minkowski inverse in Minkowski space

A Kılıçman, Z Al Zhour - Mathematical and computer modelling, 2008 - Elsevier
This paper extends some results for the weighted Moore–Penrose inverse AM, N+ in Hilbert
space to the so-called weighted Minkowski inverse AM, N⊕ of an arbitrary rectangular …

Khatri‐Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces

A Ploymukda, P Chansangiam - Journal of Mathematics, 2016 - Wiley Online Library
We introduce the notion of Khatri‐Rao product for operator matrices acting on the direct sum
of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of …

[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 …

[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] Khatri-Rao sums for Hilbert space operators

A Ploymukda, P Chansangiam - Songklanakarin J. Sci. Technol, 2018 - thaiscience.info
We generalize the notions of Khatri-Rao sums for matrices and tensor sums for Hilbert space
operators to Khatri-Rao sums for Hilbert space operators. This kind of operator sum is …

[PDF][PDF] Khatri-Rao products and selection operators

A Ploymukda, P Chansangiam - Journal of Computational …, 2019 - eudoxuspress.com
We develop further theory for Khatri-Rao products of Hilbert space operators in connections
with selection operators. We provide two constructions related to selection operators. Then …