Rank preservers of skew-symmetric matrices
نویسندگان
چکیده
منابع مشابه
On Linear Spaces of Skew-symmetric Matrices of Constant Rank
Linear sections of the Grassmannians G(1, n) of lines in P appear naturally in several different situations. In complex projective algebraic geometry, 3-dimensional linear sections of G(1, 4) appear in the classification of Fano threefolds, 2-dimensional linear sections of G(1, 5) define one of the smooth scrolls of P. Linear sections of dimension n − 1 of the Grassmannian of lines of P are cla...
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In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in Mn[R] and so(n) This paper is concerned with the following question. Let g be a Lie algebra (Carter, Segal & Macdonald 1995, Humphreys 1978, Varadarajan 1984). Given X,Y ∈ g an...
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We prove that every infinite sequence of skew-symmetric or symmetric matrices M1, M2, . . . over a fixed finite field must have a pair Mi, Mj (i < j) such that Mi is isomorphic to a principal submatrix of the Schur complement of a nonsingular principal submatrix in Mj , if those matrices have bounded rank-width. This generalizes three theorems on well-quasi-ordering of graphs or matroids admitt...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1970
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1970.35.169