Block triangularization of skew-symmetric matrices
โ Scribed by Satoru Iwata
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 414 KB
- Volume
- 273
- Category
- Article
- ISSN
- 0024-3795
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โฆ Synopsis
This paper addresses the finest block triangularization of nonsingular skewsymmetric matrices by simultaneous permutations of rows and columns. Hierarchical relations among components are represented in terms of signed posets. The finest block-triangular form can be computed efficiently with the aid of the strongly connected component decomposition of bidirected graphs.
๐ SIMILAR VOLUMES
Let R โ C mรm and S โ C nรn be nontrivial involution matrices; i.e. R = R -1 = ยฑI and S = S -1 = ยฑI. An m ร n complex matrix A is said to be a (R, S)-symmetric ((R, S)skew symmetric) matrix if RAS = A (RAS = -A). The (R, S)-symmetric and (R, S)-skew symmetric matrices have many special properties an
Let n be a positive, even integer and let K n (F ) denote the subspace of skew-symmetric matrices of Mn(F ), the full matrix algebra with coefficients in a field F. A theorem of Kostant states that K n (F) satisfies the (2n -2)-fold standard identity s 2n-2 . In this paper we refine this result by s