Maps preserving trace of products of matrices
Huajun Huang, Ming-Cheng Tsai

TL;DR
This paper characterizes certain trace-preserving maps on matrix subsets, proving their linearity and injectivity, with applications to understanding maps that preserve the trace of matrix products across various matrix classes.
Contribution
It establishes the linearity and injectivity of maps satisfying trace conditions, extending to multiple matrix classes and providing real versions.
Findings
Maps satisfying trace conditions are linear and injective.
Characterization of trace-preserving maps for various matrix types.
Extension of results to real matrix versions.
Abstract
We prove the linearity and injectivity of two maps and on certain subsets of that satisfy . We apply it to characterize maps () satisfying in which is the set of -by- general, Hermitian, or symmetric matrices for , or positive definite or diagonal matrices for . The real versions are also given.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Graph theory and applications
