The Inverse of a Centrosymmetric Matrix

I. J. Good

doi:10.1080/00401706.1970.10488743

November 1, 1970Technometrics

The Inverse of a Centrosymmetric Matrix

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Key Points

To derive an analytical and computationally efficient formulation for computing the inverse of a centrosymmetric matrix.
Examined the algebraic properties and inherent spatial symmetries of centrosymmetric matrices.
Applied similarity transformations and matrix partitioning techniques to decouple the original matrix into smaller submatrices.
Demonstrated that the inverse of a nonsingular centrosymmetric matrix remains centrosymmetric.
Established that computing the full matrix inverse reduces to inverting two smaller half-sized matrices, significantly cutting arithmetic operations.

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Implication

Mathematical analysis demonstrates an algebraic simplification for inverting centrosymmetric matrices, suggesting reduced computational effort in solving structured linear systems.

Abstract

(1970). The Inverse of a Centrosymmetric Matrix. Technometrics: Vol. 12, No. 4, pp. 925-928.

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I. J. Good (1970) studied this question.

synapsesocial.com/papers/6a9332a59b47b0854fd187b6 https://doi.org/10.1080/00401706.1970.10488743

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The Inverse of a Centrosymmetric Matrix

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Implication

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The Inverse of a Centrosymmetric Matrix

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Implication

Abstract

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