  It is well known that the product of two independent regularly varying random
variables with the same tail index is again regularly varying with this index.
In this paper, we provide sharp sufficient conditions for the regular variation
property of product-type functions of regularly varying random vectors,
generalizing and extending the univariate theory in various directions. The
main result is then applied to characterize the regular variation property of
products of iid regularly varying quadratic random matrices and of solutions to
affine stochastic recurrence equations under non-standard conditions.
