Positive linear maps on normal matrices

Linear maps preserving or strongly preserving majorization on matrices

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...

Positive Linear Maps and Spreads of Matrices

Positive linear maps and spreads of matrices-II

It is shown how positive linear maps can be used to obtain lower bounds for spreads of normal matrices. Some known results and some new ones are obtained in this way. AMS classification: 15A45, 15A60, 47A12,

linear maps preserving or strongly preserving majorization on matrices

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...

On Positive Matrices Which Have a Positive Smith Normal Form

It is known that any symmetric matrix M with entries in R[x] and which is positive semi-definite for any substitution of x ∈ R, has a Smith normal form whose diagonal coefficients are constant sign polynomials in R[x]. We generalize this result by considering a symmetric matrix M with entries in a formally real principal domain A, we assume that M is positive semi-definite for any ordering on A...