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On split r-Jacobsthal quaternions

100%

Bród D.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2020

tom 74

nr 1

In this paper we introduce a one-parameter generalization of the split Jacobsthal quaternions, namely the split r-Jacobsthal quaternions. We give a generating function, Binet formula for these numbers. Moreover, we obtain some identities, among others Catalan, Cassini identities and convolution identity for the split r-Jacobsthal quaternions.

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

86%

Taher R. B., Rachidi M.

Special Matrices

2015

tom 3

nr 1

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.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Special Matrices

1 Bród D.

1 Rachidi M.

1 Taher R. B.

1 2020

1 2015

Wyniki wyszukiwania

On split r-Jacobsthal quaternions

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