Characteristic roots of $M$-matrices

On Square Roots of M-Matrices

The question of the existence and uniqueness of an M-matrix which is a square root of an M-matrix is discussed. The results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an M-matrix.

The Roots and Links in a Class of M-matrices

In this paper, we discuss exiting roots of sub-kernel transient matrices P associated with a class of M−matrices which are related to generalized ultrametric matrices. Then the results are used to describe completely all links of the class of matrices in terms of structure of the supporting tree.

Computation of the q-th roots of circulant matrices

In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C.

A Note on the Confidence Bounds for the Characteristic Roots of Dispersion Matrices of Normal Variates

Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions

Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level ...