JOURNAL ARTICLE

Quaternion-valued exponential matrices and its fundamental properties.

  • Published In: International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics, 2023, v. 37, n. 3. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Zahid, Muhammad; Younus, Awais; Ghoneim, Mohamed E.; Yassen, Mansour F.; Haider, Jamil Abbas 3 of 3

Abstract

Quaternion differential equations (QDEs) are a new kind of differential equations which differ from ordinary differential equations. Our aim is to get the exponential matrices for the QDE which is useful for finding the solution of quaternion-valued differential equations, also, we know that linear algebra is very useful to calculate the exponential for a matrix but the solution of QDE is not a linear space. Due to the noncommutativity of the quaternion, the solution set of QDE is a right free module. For this, we must read some basic concepts on Quaternions such as eigenvalues, eigenvectors, Wronskian and the difference between quaternion and complex eigenvalues and eigenvectors; by using the right eigenvalue method for quaternions we developed a fundamental matrix which is useful to construct the exponential matrices which perform a great role in solving the QDEs. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics. 2023/01, Vol. 37, Issue 3, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2023
  • ISSN:0217-9792
  • DOI:10.1142/S0217979223500273
  • Accession Number:161063079
  • Copyright Statement:Copyright of International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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