Term rank preservers of bisymmetric matrices over semirings

On idempotent matrices over semirings

Idempotent matrices play a significant role while dealing with different questions in matrix theory and its applications. It is easy to see that over a field any idempotent matrix is similar to a diagonal matrix with 0 and 1 on the main diagonal. Over a semiring the situation is quite different. For example, the matrix J of all ones is idempotent over Boolean semiring. The first characterizatio...

Efficient transitive closure of sparse matrices over closed semirings

Tan's Epsilon-Determinant and Ranks of Matrices over Semirings

We use the ϵ-determinant introduced by Ya-Jia Tan to define a family of ranks of matrices over certain semirings. We show that these ranks generalize some known rank functions over semirings such as the determinantal rank. We also show that this family of ranks satisfies the rank-sum and Sylvester inequalities. We classify all bijective linear maps which preserve these ranks.

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...

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 :...