On the Cayley transform of positivity classes of matrices
Shaun Fallat, Michael J. Tsatsomeros · Electronic Journal of Linear Algebra · 2002
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.