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2 Special Matrices

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An effective recursive formula for the Frobenius covariants in matrix functions

100%

Schäfer F.

nr 1

113-122

For theoretical studies, it is helpful to have an explicit expression for a matrix function. Several methods have been used to determine the required Frobenius covariants. This paper presents a recursive formula that calculates these covariants effectively. The new aspect of this method is the simple determination of the occurring coefficients in the covariants. The advantage is shown by several examples for the matrix exponential in comparision with Mathematica. The calculations are performed exactly.

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

75%

Taher R. B. , Rachidi M.

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.