Bilinear transformations on matrices: Rank preservers
نویسندگان
چکیده
منابع مشابه
On higher rank numerical hulls of normal matrices
In this paper, some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated. A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given. Moreover, using the extreme points of the numerical range, the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$, where $A_1...
متن کاملEla Additive Preservers of Tensor Product of Rank One Hermitian Matrices
Let K be a field of characteristic not two or three with an involution and F be its fixed field. Let Hm be the F -vector space of all m-square Hermitian matrices over K. Let ρm denote the set of all rank-one matrices in Hm. In the tensor product space ⊗ k i=1 Hmi , let ⊗ k i=1 ρmi denote the set of all decomposable elements ⊗ k i=1 Ai such that Ai ∈ ρmi , i = 1, . . . , k. In this paper, additi...
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 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 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: 1997
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00426-2