Before revision: This paper aims at giving some equivalent conditions for that a collection of finitely many of Hermitian matrices can be simultaneously diagonalizable via congruence (SDC) by a nonsingular matrix.
After revision: This paper aims at solving the Hermitian SDC problem, i.e., that of a collection of finitely many of Hermitian matrices can be simultaneously diagonalizable via congruence (SDC) by a nonsingular matrix.