Linear preservers on spaces of hermitian or real symmetric matrices
نویسندگان
چکیده
منابع مشابه
Linear 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 کاملAdjacency preservers, symmetric matrices, and cores
It is shown that the graph Γn that has the set of all n× n symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their difference equals one, is a core if n≥ 3. Eigenvalues of the graph Γn are calculated as well.
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 کاملGeometrical phases on hermitian symmetric spaces
For simple Lie groups, the only homogeneous manifolds G/K, where K is maximal compact subgroup, for which the phase of the scalar product of two coherent state vectors is twice the symplectic area of a geodesic triangle are the hermitian symmetric spaces. An explicit calculation of the multiplicative factor on the complex Grassmann manifold and its noncompact dual is presented. It is shown that...
متن کاملTotally Positive Density Matrices and Linear Preservers
The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Hig...
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: 1993
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)90425-n