A Method of Global Blockdiagonalization for Matrix-Valued Functions
H. Gingold · SIAM Journal on Mathematical Analysis · 1978
Let $A(x)$ be an $n \times n$ analytic matrix function of the vector variable x. Let the eigenvalues of $A(x)$ belong to two disjoint sets for every fixed x. Then there exists an invertible analytic matrix function $M(x)$ which takes $A(x)$ by a similarity transformation into a blockdiagonal form. Similar theorems for $A(x)$ being smooth are also proved.