Trace and determinant preserving maps of matrices

Huajun Huang, Chih-Neng Liu, Patricia Szokol +2

Suppose a map $\varphi$ on the set of positive definite matrices satisfies $\det (A+B)=\det (\varphi (A)+\varphi (B))$. Then we have $$\mathrm{tr}(A{B}^{-1})=\mathrm{tr}(\varphi (A){\varphi (B)}^{-1}).$$ Through this viewp…