Several general techniques on linear preserver problems are described. The first one is based on a transfer principle in Model Theoretic Algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0. The second one concerns the use of some simple geometric technique to reduce linear preserver problems to sta...

For two bipartite graphs G and G , a bijection ψ : E(G) → E(G) is called a (perfect) matching preserver provided that M is a perfect matching in G if and only if ψ(M) is a perfect matching in G. We characterize bipartite graphs G and G which are related by a matching preserver and the matching preservers between them.

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

If you are in a shipwreck and all the boats are gone, a piano top...that comes along makes a fortuitous life preserver. But this is not to say that the best way to design a life preserver is in the form of a piano top. I think that we are clinging to a great many piano tops in accepting yesterday’s fortuitous contrivings as constituting the only means for solving a given problem. (Fuller 1969, ...

We examine a novel proposal wherein a user who hands off her data to a web service has complete choice over the code and policies that constrain access to her data. Such an approach is possible if the web service does not require raw access to the user’s data to implement its functionality; access to a carefully chosen interface to the data suffices. Our data preserver framework rearchitects su...

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

Norm preserver maps of Jordan product on the algebra Mn of n×n complex matrices are studied, with respect to various norms. A description of such surjective maps with respect to the Frobenius norm is obtained: Up to a suitable scaling and unitary similarity, they are given by one of the four standard maps (identity, transposition, complex conjugation, and conjugate transposition) on Mn, except ...