Linear Algebra

Conjecture : Any complex or real matrix is the sum of two unitary matrices. Proof (ideas) : We know that every complex matrix A could be diagonalized using two unitary matrices U and V : $$ A = UDV^{*} $$ . The matrix D has positive elements : D=diag(d1,…d2) with $$d_1\geq d_2 \geq …\geq d_n \geq 0$$. A basic result is the following : every diagonal matrix could be diagonalized with n unitary matrix. »