COMPUTING CAUCHY INTEGRAL THEOREM OF A MATRIX FUNCTION VIA SIMILARITY TRANSFORMATION AND BEHAVIOR OF HYPERGEOMETRIC MATRIX DENSITY FUNCTION

Authors

  • Stephen Ehidiamhen Uwamusi Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Edo State, Nigeria. Author

Keywords:

65F60, 65F15, Secondary, 30E20, 28A25, primary 28A20, density of a matrix MSC 2020 (Mathematical Reviews and zbMath), Bessel matrix polynomial, hypergeometric function, Cauchy integral matrix function

Abstract

It is shown that Cauchy integral matrix function is Lebesgue measurable on the contour integral based on the Little Wood’s third formula for which the trapezoidal rule and Simpson composite method are applicable. As a follow up, it is demonstrated that Taylor series representation of Cauchy integral matrix function is commutable with similarity matrix transformation when Jordan canonical block along diagonal is taken into consideration. The spectrum of the diagonalizable matrix A is computed using the Givens
orthogonal matrix plane rotation. As an extension of ideas; a measure of effectiveness on the use of SVD in the computation process is emphasized and fully utilized which leads to demonstration with the exponential of a matrix function as an example. Further analytical reasoning on performance of Cauchy integral theorem for the matrix functional calculus leads to the method of Residue theorem. The
density of a matrix function is calculated based on the hypergeometric series taking into consideration the behavior of gamma function. 

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Published

2022-12-01

How to Cite

COMPUTING CAUCHY INTEGRAL THEOREM OF A MATRIX FUNCTION VIA SIMILARITY TRANSFORMATION AND BEHAVIOR OF HYPERGEOMETRIC MATRIX DENSITY FUNCTION. (2022). The Transactions of the Nigerian Association of Mathematical Physics, 18, 87-100. https://nampjournals.org.ng/index.php/tnamp/article/view/166

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