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

Special Matrices (2015)

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

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topR. 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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