George A. Hagedorn and Caroline Lasser Symmetric Kronecker products and semiclassical wave packets (40K, latex) ABSTRACT. We investigate the iterated Kronecker product of a square matrix with itself and prove an invariance property for symmetric subspaces. This motivates the definition of an iterated symmetric Kronecker product and the derivation of an explicit formula for its action on vectors. We apply our result for describing a linear change in the matrix parametrization of semiclassical wave packets.