Automorphisms of M, partially ordered by rank subtractivity ordering

Legiša, Peter

doi:10.1016/j.laa.2004.03.024

Cited by 19 publications

(8 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Following this idea Legiša [38] recently characterized surjective maps on matrix algebras preserving minus partial ordering in both directions. It is interesting to note that such maps are automatically semilinear.…”

Section: Proof Of Proposition 42mentioning

confidence: 99%

Maps on matrix spaces

Šemrl

2006

Linear Algebra and its Applications

View full text Add to dashboard Cite

It is well known that every automorphism of the full matrix algebra is inner. We give a short proof of this statement and discuss several extensions of this theorem including structural results for multiplicative maps on matrix algebras, characterizations of monotone and orthogonality preserving maps on idempotent matrices, some nonlinear preserver results, and some recent theorems concerning geometry of matrices. We show that all these topics are closely related and point out the connections with physics and geometry. Several open problems are posed.

show abstract

Section: Proof Of Proposition 42mentioning

confidence: 99%

Maps on matrix spaces

Šemrl

2006

Linear Algebra and its Applications

View full text Add to dashboard Cite

show abstract

“…Moreover, the minus partial order was introduced by Hartwig in [11] and independently by Nambooripad in [27] on a general regular semigroup however it was mostly studied on M n (F) (see [23] and the references therein). More recently, Šemrl generalized in [34] this order to B(H), the algebra of all bounded linear opearators on a Hilbert space H, and studied preservers of this order (see also [18]). Let A be some subset of B(H) and denote by ≤ one of the above orders (i.e.…”

Section: Introductionmentioning

confidence: 99%

Preservers of partial orders on the set of all variance-covariance matrices

Golubić

Marovt

2020

Filomat

View full text Add to dashboard Cite

Let H+n(R) be the cone of all positive semidefinite n x n real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the L?wner and the minus partial orders. Motivated by applications in statistics we study these partial orders on H+n(R). We describe the form of all surjective maps on H+ n (R), n > 1, that preserve the L?wner partial order in both directions. We present an equivalent definition of the minus partial order on H+n(R) and also characterize all surjective, additive maps on H+ n (R), n ? 3, that preserve the minus partial order in both directions.

show abstract

“…In .b/ ) .a/, we have shown that x that has the forms of (16) and (17) are solutions of the system (2). So we only need to prove that for an arbitrary solution x 0 of the system (2) can be expressed as the forms of (16) and (17). Set…”

Section: Introductionmentioning

confidence: 99%

“…That is, any solution of (2) can be represented by (16) and (17). Thus (16) and (17) are the general solutions of (2).…”

Section: Introductionmentioning

confidence: 99%