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Analytic inversion for a general case of certain classes of matrices. (English) Zbl 0937.65029
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.
MSC:
65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
65F40Determinants (numerical linear algebra)
15A09Matrix inversion, generalized inverses
15A15Determinants, permanents, other special matrix functions