Maps on spaces of symmetric matrices preserving idempotence
The authors classify maps on \(n\)-by--\(n\) symmetric matrices, over rather general fields, with the property that \(A-\lambda B\) is idempotent precisely when \(\Phi(A)-\lambda\Phi(B)\) is. No linearity nor surjectivity/injectivity of \(\Phi\) is part of the hypothesis. It is assumed that \(n\geq 4\), the underlying field has at least \(5\) elements, and that its characteristics differs from \(2\).
scientific article; zbMATH DE number 5083626