# Determinantal Representations of Solutions to Systems of Quaternion Matrix Equations

Determinantal Representations of Solutions to Systems of Quaternion Matrix Equations Within the framework of the theory of quaternion column–row determinants and using determinantal representations of the Moore–Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of solutions (analogs of Cramer’s rule) to the systems of quaternion matrix equations $$\mathbf{A}_{1}{} \mathbf{X}=\mathbf{C}_{1}$$ A 1 X = C 1 , $$\mathbf{X}\mathbf{B}_{2}=\mathbf{C}_{2}$$ X B 2 = C 2 , and $$\mathbf{A}_{1}{} \mathbf{X}=\mathbf{C}_{1}$$ A 1 X = C 1 , $$\mathbf{A}_{2} \mathbf{X}=\mathbf{C}_{2}$$ A 2 X = C 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

# Determinantal Representations of Solutions to Systems of Quaternion Matrix Equations

, Volume 28 (1) – Feb 23, 2018
16 pages

/lp/springer_journal/determinantal-representations-of-solutions-to-systems-of-quaternion-NljQuz0BIR
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
D.O.I.
10.1007/s00006-018-0843-1
Publisher site
See Article on Publisher Site

### Abstract

Within the framework of the theory of quaternion column–row determinants and using determinantal representations of the Moore–Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of solutions (analogs of Cramer’s rule) to the systems of quaternion matrix equations $$\mathbf{A}_{1}{} \mathbf{X}=\mathbf{C}_{1}$$ A 1 X = C 1 , $$\mathbf{X}\mathbf{B}_{2}=\mathbf{C}_{2}$$ X B 2 = C 2 , and $$\mathbf{A}_{1}{} \mathbf{X}=\mathbf{C}_{1}$$ A 1 X = C 1 , $$\mathbf{A}_{2} \mathbf{X}=\mathbf{C}_{2}$$ A 2 X = C 2 .

### Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Feb 23, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations