On the Cayley transform of positivity classes of matrices
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چکیده
The Cayley transform of A, F = (I+A)−1 (I−A), is studied when A is a P -matrix, an M -matrix, an inverse M-matrix, a positive definite matrix, or a totally nonnegative matrix. Given a matrix A in each of these positivity classes and using the fact that the Cayley transform is an involution, properties of the ensuing factorization A = (I+F )−1 (I−F ) are examined. Specifically, it is investigated whether these factors belong to the same positivity class as A and, conversely, under what conditions on these factors does A belong to one of the above positivity classes.
منابع مشابه
Ela on the Cayley Transform of Positivity Classes of Matrices∗
The Cayley transform of A, F = (I+A)−1 (I−A), is studied when A is a P -matrix, an M -matrix, an inverse M-matrix, a positive definite matrix, or a totally nonnegative matrix. Given a matrix A in each of these positivity classes and using the fact that the Cayley transform is an involution, properties of the ensuing factorization A = (I+F )−1 (I−F ) are examined. Specifically, it is investigate...
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تاریخ انتشار 2017