Spaces of symmetric matrices of bounded rank
نویسندگان
چکیده
منابع مشابه
Primitive Spaces of Matrices of Bounded Rank
A weak canonical form is derived for vector spaces of m x n matrices all of rank at most r. This shows that the structure of such spaces is controlled by the structure of an associated 'primitive' space. In the case of primitive spaces it is shown that m and n are bounded by functions of r and that these bounds are tight. 1980 Mathematics subject classification (Amer. Math. Soc.): 15 A 30, 15 A...
متن کاملSpaces of Matrices of Bounded Rank
IN this paper we shall consider matrices over a field F and shall prove the following result: THEOREM. Let M be a 2-dimensional space o/mxn matrices with the property that rank (X) *£ k < \F\ for every XeM. Then there exist two integers r, s, O^r, s *£ fc with r + s = k, and two non-singular matrices P, Q such that, for all XeM, PXQ has the form Notice that a matrix of the above form necessaril...
متن کاملLinear spaces and preservers of bounded rank-two per-symmetric triangular matrices
Let F be a field and m,n be integers m,n > 3. Let SMn(F) and STn(F) denote the linear space of n × n per-symmetric matrices over F and the linear space of n × n per-symmetric triangular matrices over F, respectively. In this note, the structure of spaces of bounded rank-two matrices of STn(F) is determined. Using this structural result, a classification of bounded rank-two linear preservers ψ :...
متن کاملOn 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...
متن کاملWeakly Symmetric Spaces and Bounded Symmetric Domainshieu
In this paper, new examples of weakly symmetric spaces in the sense of A. Selberg 14] are constructed. Let G be a connected, simply-connected, simple Lie group of hermitian type and K a maximal compactly embedded subgroup of G such that D = G=K is an irreducible classical bounded symmetric domain. Let G 1 and D 1 be circle extensions of G and D, respectively. The factor of automorphy induces a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90488-x