In this note a matrix version of the q-d algorithm is introduced. It is shown that the algorithm may be used to obtain the coeÆcients of the recurrence relations for matrix orthogonal polynomials on the interval [0,∞) and [0;1] from its moment generating functional. The algorithm is...

In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2 where N is the sample size. The test statistic is based on the smallest estimated...