ELA, Volume 9, pp. 190-196, September 2002, abstract.
On the Cayley Transform of Positivity Classes
of Matrices
Shaun M. Fallat and Michael J. Tsatsomeros
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.