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The antitriangular factorization of skew-symmetric matrices

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  • Singer, Sanja

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.

Suggested Citation

  • Singer, Sanja, 2020. "The antitriangular factorization of skew-symmetric matrices," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    • Handle: RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302320
    DOI: 10.1016/j.amc.2020.125263
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    Cited by:

    1. Wu, Yunyun & Li, Yayun, 2023. "Anti-diagonalization theory and algorithm of matrices—from skew-symmetric matrices to arbitrary matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 44-54.

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