Journal ArticleDOI
Linear Operations on Matrices
TLDR
In this paper, a linear operation on matrices is presented. But linear operations on matrix do not have a linear operator and linear operations cannot be expressed as linear operations, either.Abstract:
(1962). Linear Operations on Matrices. The American Mathematical Monthly: Vol. 69, No. 9, pp. 837-847.read more
Citations
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Linear preserver problems: A brief introduction and some special techniques
Chi-Kwong Li,Nam-Kiu Tsing +1 more
TL;DR: Linear preserver problems as discussed by the authors concern the characterization of linear operators on matrix spaces that leave certain functions, subsets, relations, etc., invariant, and a great deal of effort has been devoted to the study of this type of question since then.
Journal ArticleDOI
Commuting maps: a survey
TL;DR: In this article, the authors survey the development of the theory of commuting maps and their applications, including derivations, commuting additive maps, commuting traces of multiadditive maps, various generalizations of the notion of a commuting map, and applications of results on commuting maps to Lie theory.
Journal ArticleDOI
Linear transformations on matrices
TL;DR: In this paper, it was shown that the problem of finding the invariant I can be expressed as a scalar valued fun ction, e.g., I(X) = det (X) ; or for that matter it can describe a property of I (X), i.e., m can equal M\" (C) and I(x) can mean that X is unitary, so that we are simply asking for the s tructure of all linear transformation s T that map the unitary group into itself.
References
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Journal ArticleDOI
On the similarity transformation between a matirx and its transpose.
Olga Taussky,Hans Zassenhaus +1 more
Journal ArticleDOI
Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
Marvin Marcus,Roger Purves +1 more
TL;DR: In this paper, the structure of certain linear transformations T on the algebra of w-square matrices Mn into itself was examined and the main result was that if 4 ≤ r ≤ n 1 and Er(T(A)) = Er(A) for A ∈ Mn then T is essentially (modulo taking the transpose and multiplying by a constant) a similarity transformation.