Volume 7, Issue 7 (July 2020), Pages: 92-94

----------------------------------------------

 Short Communication

 Title: The square root of tridiagonal Toeplitz matrices

 Author(s): Ismaiel Krim ^{1, 2,} *, Mohamed Tahar Mezeddek ^{1, 2}, Abderrahmane Smail ^{1, 2}

 Affiliation(s):

 ¹Département de Mathématiques, Faculté des Sciences Exactes et Appliquées, Université Oran 1, Oran, Algérie
 ²Laboratory of Geometry and Analysis – GENLAB, Oran 1 University, Algeria

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-3033-512X

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.07.011

 Abstract:

In this paper, we present an explicit formula to find square roots of a tridiagonal Toeplitz matrix, and we show that these square roots have the form of a persymmetric matrix with examples to illustrate. 

 © 2020 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Tridiagonal, Toeplitz matrix, Square root, Persymmetric matrix, Eigenvalue

 Article History: Received 15 December 2019, Received in revised form 10 April 2020, Accepted 21 April 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The authors declare that they have no conflict of interest.

 Citation:

 Krim I, Mezeddek MT, and Smail A (2020). The square root of tridiagonal Toeplitz matrices. International Journal of Advanced and Applied Sciences, 7(7): 92-94

 Permanent Link to this page

 Figures

 No Figure

 Tables

 No table

----------------------------------------------

 References (4)

1. Meyer CD (2000). Matrix analysis and applied linear algebra. Volume 71, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA. https://doi.org/10.1137/1.9780898719512   [Google Scholar]
2. Noschese S, Pasquini L, and Reichel L (2013). Tridiagonal Toeplitz matrices: Properties and novel applications. Numerical Linear Algebra with Applications, 20(2): 302-326. https://doi.org/10.1002/nla.1811   [Google Scholar]
3. Salkuyeh DK (2006). Positive integer powers of the Tridiagonal Toeplitz matrices. International Mathematical Forum, 1: 1061-1065. https://doi.org/10.12988/imf.2006.06086   [Google Scholar]
4. Yuttanan B and Nilrat C (2005). Roots of matrices. Songklanakarin Journal of Science and Technology, 27(3): 659-665.   [Google Scholar]