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CM–fields and skew–symmetric matrices

✍ Scribed by Eva Bayer-Fluckiger; Grégory Berhuy; Pascale Chuard–Koulmann


Publisher
Springer
Year
2004
Tongue
English
Weight
110 KB
Volume
114
Category
Article
ISSN
0025-2611

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Let R ∈ C m×m and S ∈ C n×n be nontrivial involution matrices; i.e. R = R -1 = ±I and S = S -1 = ±I. An m × 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

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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

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✍ Jordan Dale Hill 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 137 KB

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