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 $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

Linear preserver problems is an active research area in matrix and operator theory. These problems involve certain linear operators on spaces of matrices or operators. We give a general introduction to the subject in this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss ...

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

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...

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...

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