A complete classification of additive rank–one nonincreasing maps on hermitian matrices over Galois field GF (22) is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank–additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieti...

In smallholder agriculture, women farmers are largely responsible for the selection, improvement and adaptation of plant varieties. In many regions, women are also responsible for the management of small livestock, including their reproduction. Women often have a more highly specialized knowledge of wild plants used for food, fodder and medicine than men. Women – users, preservers and managers ...

Let $X$ be a finite connected poset, $F$ field and $I(X,F)$ the incidence algebra of over $F$. We describe bijective linear idempotent preservers $\varphi:I(X,F)\to I(X,F)$. Namely, we prove that, whenever $\mathrm{char}(F)\ne 2$, $\varphi$ is either an automorphism or anti-automorphism $I(X,F)$. If $\mathrm{char}(F)=2$ $|F|>2$, then (in general, non-proper) Lie Finally, if $F=\mathbb{Z}_2$, co...

Preservers and additive spanners are sparse (hence cheap to store) subgraphs that preserve the distances between given pairs of nodes exactly or with some small additive error, respectively. Since real-world networks are prone to failures, it makes sense to study fault-tolerant versions of the above structures. This turns out to be a surprisingly difficult task. For every small but arbitrary se...

For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the Brauer region in terms of Cassini ovals, and the Ostrowski region. Characterization is obtained for maps Φ on n × n matrices satisfying S(Φ(A) − Φ(B)) = S(A − B) for all matrices A and B. From these results, one can deduce the structure of additive or (real) linear maps satisfying S(A) = S(Φ(A)) fo...

Let Mn,m be the set of all n × m matrices with entries in F, where F is the field of real or complex numbers. A matrix R ∈ Mn with the property Re=e, is said to be a g-row stochastic (generalized row stochastic) matrix. Let A,B∈ Mn,m, so B is said to be gw-majorized by A if there exists an n×n g-row stochastic matrix R such that B=RA. In this paper we characterize all linear operators that stro...

It is shown that the linear group of automorphism of Hermitian matrices which preserves the tensor product of unitary orbits is generated by natural automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. The result is then applied to show that automorphisms of the product numerical...