Uniform Sample Generations from Contractive Block Toeplitz Matrices

This note deals with generating a series of random matrices uniformly and independently from contractive lower triangular block Toeplitz (LTBT) matrices. All the contractive LTBT matrices are parameterized nonlinearly but recursively in a closed-form by a sequence of contractive unstructured matrices. Moreover, the conditional probability density function (PDF) is obtained in a closed-form for all the matrix parameters, as well as the squares of their singular values. It has been made clear that the conditional PDFs of the matrix parameters are unitarily invariant. A procedure is developed to accurately produce the required random matrix samples.