Linear mappings on second symmetric product spaces that Preserve rank less than or equal to one

1990/02/01 by M. H. Lim · 1 citation
Mathematics · Computer Science · #Advanced Topics in Algebra #Advanced Banach Space Theory #Matrix Theory and Algorithms

paper · doi:10.1080/03081089008817975

Abstract

In this paper we characterize those linear mappings from a second symmetric product space to another which preserve decomposable elements of the form λu[sdot]u where u is a vector and λ is a scalar. This leads to the corresponding result concerning linear mappings from one vector space of symmetric matrices to another which preserve rank less than or equal to one. We also discuss some consequences of this characterization theorem.

Citations

• Linear transformations on symmetric matrices

Cited by

• Decomposability preserving linear maps between symmetric spaces

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