Explicit formulas for the constituent matrices. Application to the matrix functions

• Autorzy: R. Ben Taher , M. Rachidi
• Języki publikacji: EN

Abstrakty

EN

We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences. Some connections with other results are supplied. Furthermore,we manage to provide tractable expressions for the matrix functions, and for illustration purposes we establish compact formulas for both the matrix logarithm and the matrix pth root. Some examples are also provided.

Słowa kluczowe

EN

Generalized Fibonacci sequences; Binet formula; Constituents matrices; matrix function; Matrixlogarithm; Matrix pth root

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-11-11

zaakceptowano

2015-03-12

online

2015-03-23

Twórcy

autor

R. Ben Taher

• Département de Mathématiques et Informatique, Faculté des Sciences,Université Moulay Ismail, B.P. 4010, Beni
  M’hamed, Méknés, Morocco

autor

M. Rachidi

• Associate researcher with "Equip of DEFA", Département de Mathématiques
  et Informatique, Faculté des Sciences,Université Moulay Ismail, B.P. 4010, Beni M’hamed, Méknés, Morocco

Bibliografia

• [1] J. Abderramán Marrero, R. Ben Taher and M. Rachidi, On explicit formulas for the principal matrix logarithm, AppliedMathematics and Computation Vol. 220 (2013), p. 142-148.[WoS]
• [2] J. Abderramán Marrero, R. Ben Taher, Y. El Khattabi and M. Rachidi, On explicit formulas of the principal matrix p − th rootby polynomial decompositions, Applied Mathematics and Computation Vol. 242 (2014), p. 435-443.[WoS]
• [3] R. Ben Taher and M. Rachidi, Linear matrix differential equations of higher-order and applications, Electronic Journal ofDifferential Equations Vol. 2008 No.95 (2008), p.1-12.
• [4] R. Ben Taher and M. Rachidi, On the matrix powers and exponential by r-generalized Fibonacci sequences methods: thecompanion matrix case, Linear Algebra and Its Applications Vol. 370 (2003), p. 341-353.
• [5] R. Ben Taher and M. Rachidi, Linear recurrence relations in the algebra matrices and applications, Linear Algebra and ItsApplications Vol. 330 (2001), p. 15-24.
• [6] R. Ben Taher, I. Bensaoud and M. Rachidi; Dynamic solutions and computation of the powers and exponential of matrix,International Journal of Mathematics, Game Theory and Algebra Vol. 13 No. 6 (2003), p. 455-463.
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Identyfikatory

DOI

10.1515/spma-2015-0004