In this paper, the notion of vector-valued wavelet packets for space L (R~n)~s is introduced, which are generalizations of univariate wavelet packets. A constructive method for a class of biorthogonal vector-valued multivariate wavelet packets is presented and their biorthogonality properties are characterized by virtue of matrix theory, and operator theory. Three biorthogonality formulas concerning these wavelet packets are provided. Furthermore, new Riesz bases of space L~2(R~n)~s from these wavelet packets are obtained.
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