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Some structural properties of inverse matrices

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Abstract

The connection of some structural properties of inverse matrices such as the presence of an invertible submatrix or of a rectangular submatrix of incomplete rank is investigated. Explicit relations are obtained between the ranks of dual submatrices. The results are applied to describe the inverse to generalized Hessenberg and band matrices.

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Authors
  1. L. Yu. Kolotilina
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 139, pp. 61–73, 1984.

The author is glad to express his gratitude to D. K. Faddeev for his attention to the work.

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Kolotilina, L.Y. Some structural properties of inverse matrices. J Math Sci 36, 215–224 (1987). https://doi.org/10.1007/BF01091802

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