  In the study of determinant formulas for Schur functions, Hamel and Goulden
introduced a class of Giambelli-type matrices with respect to outside
decompositions of partition diagrams, which unify the Jacobi-Trudi matrices,
the Giambelli matrices and the Lascoux-Pragacz matrices. Stanley determined the
Smith normal form of a specialized Jacobi-Trudi matrix. Motivated by Stanley's
work, we obtain the Smith normal form of a specialized Giambelli matrix and a
specialized Lascoux-Pragacz matrix. Furthermore, we show that, for a given
partition, the Smith normal form of any specialized Giambelli-type matrix can
be obtained from that of the corresponding specialization of the classical
Giambelli matrix by a sequence of stabilization operations.
