The antitriangular factorization of skew-symmetric matrices

08/30/2019

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by   Sanja Singer, et al.

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In this paper we develop algorithms for 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, antitriangular form is always obtained. Moreover, simple two-sided permutation of the antitriangular form transforms the matrix into multi-arrowhead matrix. In addition, we show here that the block antitriangular form of the skew-Hermitian matrices has the same structure as the block antitriangular form of the symmetric matrices.