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Zbl 0937.65029
Valvi, F.N.
Analytic inversion for a general case of certain classes of matrices. (English)
[J] Int. J. Comput. Math. 72, No.2, 199-205 (1999). ISSN 0020-7160; ISSN 1029-0265/e

There is a limited number of known matrices whose inverses can be written analytically. In this paper, the explicit inverses and determinants of a new class of matrices is presented. The Hadamard product of two matrices with specific structures generates the proposed class of matrices. This class is defined by $4n-2$ parameters, and their inverses can be expressed analytically by upper Hessenberg forms. It is shown that by restricting some of the parameters the proposed test matrices become special cases of well known test matrices with explicit analytic inverses.
[R.P.Tewarson (Stony Brook)]

MSC 2000:: *65F05 Direct methods for linear systems
65F40 Determinants (numerical linear algebra)
15A09 Matrix inversion
15A15 Special matrix functions

Keywords: analytic inversion; test matrices; Hessenberg forms; explicit inverses; determinants; Hadamard product

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