abstract. let mn;m be the set of n-by-m matrices with entries inthe field of real numbers. a matrix r in mn = mn;n is a generalizedrow substochastic matrix (g-row substochastic, for short) if re e, where e = (1; 1; : : : ; 1)t. for x; y 2 mn;m, x is said to besgut-majorized by y (denoted by x sgut y ) if there exists ann-by-n upper triangular g-row substochastic matrix r such thatx = ry . th...

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.

Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate an...

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...