A generalization of a class of matrices: analytic inverse and determinant (Q666390)
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scientific article; zbMATH DE number 6013002
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalization of a class of matrices: analytic inverse and determinant |
scientific article; zbMATH DE number 6013002 |
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A generalization of a class of matrices: analytic inverse and determinant (English)
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8 March 2012
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Summary: The aim of this paper is to present the structure of a class of matrices that enables explicit inverses to be obtained. Starting from an already known class of matrices, we construct a Hadamard product that derives the class under consideration. The latter are defined by \(4n - 2\) parameters, analytic expressions of which provide the elements of the lower Hessenberg form inverse. Recursion formulae of these expressions reduce the arithmetic operations in evaluating the inverse to \(\mathcal O(n^2)\).
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matrices
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explicit inverse
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Hadamard product
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lower Hessian form inverse
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recursion formulae
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determinant
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