| Let P(x) denote a 2¡Ñ2 symmetric matrix-valued function defined on [0,1]. We prove that if there exists an infinite sequence of Dirichlet eigenfunctions {y(x; )} of¡Ð ¡ÏP(x), whose components have all zeros in common for each n N, then P(x) is simultaneously diagonalizable on [0,1]. This result can also be generalized to general n-dimensional case. |