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

R. Ben Taher; M. Rachidi

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 43-52, electronic only
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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R. Ben Taher, and M. Rachidi. "Explicit formulas for the constituent matrices. Application to the matrix functions." Special Matrices 3.1 (2015): 43-52, electronic only. <http://eudml.org/doc/270030>.

@article{R2015,
abstract = {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.},
author = {R. Ben Taher, M. Rachidi},
journal = {Special Matrices},
keywords = {Generalized Fibonacci sequences; Binet formula; Constituents matrices; matrix function; Matrix logarithm; Matrix pth root; generalized Fibonacci sequences; constituents matrices; matrix logarithm; matrix -th root},
language = {eng},
number = {1},
pages = {43-52, electronic only},
title = {Explicit formulas for the constituent matrices. Application to the matrix functions},
url = {http://eudml.org/doc/270030},
volume = {3},
year = {2015},
}

TY - JOUR
AU - R. Ben Taher
AU - M. Rachidi
TI - Explicit formulas for the constituent matrices. Application to the matrix functions
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 43
EP - 52, electronic only
AB - 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.
LA - eng
KW - Generalized Fibonacci sequences; Binet formula; Constituents matrices; matrix function; Matrix logarithm; Matrix pth root; generalized Fibonacci sequences; constituents matrices; matrix logarithm; matrix -th root
UR - http://eudml.org/doc/270030
ER -

References

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