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.

中文翻译：

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偏对称矩阵的反三角分解

在本文中，我们开发了将偏对称矩阵相似变换为更简单形式的算法。第一种算法类似于对称矩阵的块反三角分解算法，但在偏对称矩阵的情况下，总是得到反三角形式。此外，反三角形式的简单两侧置换将矩阵转换为多箭头矩阵。此外，我们在这里展示了偏斜 Hermitian 矩阵的块反三角形式与对称矩阵的块反三角形式具有相同的结构。