Spectral Radius Inequalities of the Kronecker Product of Nonnegative Random Matrices
WU Zhu-wu · Journal of China University of Mining and Technology · 2008
The representations of the elements of the Kronecker product for random matrices were obtained.The expectation values of the Kronecker product for nonnegative random matrices were studied.Inequalities between the expected values of the Kronecker product and the Kronecker product of the expected values were established.Several inequalities of the spectral radius of the Kronecker product for nonnegative random matrices were derived.These derivations rely on the properties of expectation and the Kronecker product and the choice of norm used to represent the spectral radius of the matrix as a limiting form.The main results include inequalities of matrix functions and inequalities of block matrices.Furthermore,two examples are given to show the application of the main results to nonlinear time series models.