منابع مشابه
On pth roots of stochastic matrices
In Markov chain models in finance and healthcare a transition matrix over a certain time interval is needed but only a transition matrix over a longer time interval may be available. The problem arises of determining a stochastic pth root of a stochastic matrix (the given transition matrix). By exploiting the theory of functions of matrices, we develop results on the existence and characterizat...
متن کاملA Note on the Stochastic Roots of Stochastic Matrices
In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2¥2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3¥3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical met...
متن کاملComputation 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.
متن کاملOn Hadamard Matrices at Roots of Unity
Abstract. We study Hadamard matrices of order n, formed by l-th roots of unity. A main problem is to find the allowed values of (n, l), and we discuss here the following statement: for l = pa 1 . . . pa s we must have n ∈ p1+. . .+psN. For s = 1 this is a previously known result, for s = 2, 3 this is a result that we prove in this paper, and for s ≥ 4 this is a conjecture that we raise. We pres...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.04.007