Geodesic
On the Cayley transform of positivity classes of matrices
The electronic journal of linear algebra, Tome 9 (2002), pp. 190-196.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 15A23, 15A24, 15A48
Keywords: Cayley transform, P -matrices, M-matrices, positive definite matrices, totally nonnegative matrices, stable matrices, matrix factorizations 
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     title = {On the {Cayley} transform of positivity classes of matrices},
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Fallat, Shaun M.; Tsatsomeros, Michael J. On the Cayley transform of positivity classes of matrices. The electronic journal of linear algebra, Tome 9 (2002), pp. 190-196. http://geodesic.mathdoc.fr/item/ELA_2002__9__a5/