Additive rank-one preservers on block triangular matrix spaces

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 :...

Ela 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...

On Nonlinear Preservers of Weak Matrix Majorization

Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CHn, n ≥ 3. For the quaternionic hyperbolic spaces HHn, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificat...

Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix ...