Adjacency preserving mappings on real symmetric matrices

Let $S_{n}$ denote the space of all $n \times n$ real symmetric matrices. For n=2 or n>2 we characterize maps F from $S_{n}$ to $S_{m}$ which preserve adjacency, i.e. if rank(A-B)=1, then rank(F(A)-F(B))=1.

💡 Research Summary

The paper investigates maps between spaces of real symmetric matrices that preserve adjacency, where two matrices are called adjacent if the rank of their difference equals one. Let (S_n) denote the set of all (n\times n) real symmetric matrices and consider a map (\Phi:S_n\to S_m) with the property that
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