The antitriangular factorization of skew-symmetric matrices

Sanja Singer

doi:10.1016/j.amc.2020.125263

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arXiv · 1909.00092

The antitriangular factorization of skew-symmetric matrices

Sanja Singer

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Abstract

In this paper we develop algorithms for orthogonal similarity transformations of skew-symmetric matrices to simpler forms. The first algorithm is similar to the algorithm for the block antitriangular factorization of symmetric matrices, but in the case of skew-symmetric matrices, an antitriangular form is always obtained. Moreover, a simple two-sided permutation of the antitriangular form transforms the matrix into a multi-arrowhead matrix. In addition, we show that the block antitriangular form of the skew-Hermitian matrices has the same structure as the block antitriangular form of the symmetric matrices.

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Sanja Singer. 2019-08-30. The antitriangular factorization of skew-symmetric matrices. https://doi.org/10.1016/j.amc.2020.125263

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