Baodong Zheng

Moore–Penrose inverse of tensors via Einstein product

In this paper, we define the Moore–Penrose inverse of tensors with the Einstein product, and the explicit formulas of the Moore–Penrose inverse of some block tensors are obtained. The general solutions of some multilinear systems are given and we also give the minimum-norm least-square solution of some multilinear systems using the Moore–Penrose inverse of tensors.

Linear maps preserving rank of tensor products of matrices

Let be the algebra of all complex matrices. We characterize linear maps satisfyingfor all , .

Characterizations of the spectral radius of nonnegative weakly irreducible tensors via a digraph

For a nonnegative weakly irreducible tensor , we give some characterizations of the spectral radius of , by using the digraph associated with the tensor . As applications, some bounds on the spectral radius of the adjacency tensor and the signless Laplacian tensor of a k-uniform hypergraph are obtained.

Nonlinear mappings preserving Jordan multiple *- product on factor von Neumann algebras

Let and be two factor von Neumann algebras. For define by the Jordan multiple product in any fixed operation order. In this article, it is proved that a not necessarily linear bijective mapping satisfies if and only if is a ring isomorphism. In particular, if the von Neumann algebras and are type I factors, then is a unitary isomorphism or a conjugate unitary isomorphism.

LINEAR MAPS PRESERVING TENSOR PRODUCTS OF RANK-ONE HERMITIAN MATRICES

For a positive integer

Some inequalities for the Hadamard product of tensors

n\geq 2

Algebraic Lyapunov and Stein stability results for tensors

, let

Sensitivity analysis of the Lyapunov tensor equation

M_{n}

Idempotence preserving maps between matrix spaces

be the set of

Linear maps preserving idempotents of tensor products of matrices

n\times n