Heyman gives an interesting factorization of I ? P , where P is the transition probability matrix for an ergodic Markov Chain. We show that this factoriza-tion is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to...

In this paper, the UDUT decomposition of the generalized inertia matrix o f an n-link serial manipulator is presented in symbolic form, where U and D, respectively, are the upper triangular and diagonal matrices. To render the decomposition, the elementary upper triangular matrices, associated to a modified Gaussian elimination, are introduced, whereas each element of the inertia matrix is writ...

Superregular matrices are a type of lower triangular Toeplitz matrix that arises in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that the only submatrices having a zero determinant are those whose determinants are trivially zero due to the lower triangular structure. In this paper, we discuss how superregular...

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials ∏ tr ( X1ΩY 1ΩX2 · · · ) with the weight exp tr ( XΩY Ω ) are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries)...

We parametrize the space of double cosets group GL(n,k) with respect to two subgroups T−, T+ block strictly triangular matrices. In appendix, we consider quasi-regular representation GL(n,C) in L2 on T−∖GL(n,C), observe that it admits an additional symmetries, find joint spectrum, and is multiplicity free.

It is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered. c © 2007 Elsevier Ltd. All rights reserved.