On Mon, Mar 28, 2011 at 3:15 PM, Thomas Colthurst <thomaswc@gmail.com> wrote:
http://mathoverflow.net/questions/50120/eigenvalues-of-matrix-product implies that the product of two Hermitian matrices is diagonalisable with real eigenvalues of the same signs as the second factor, and gives Prop 6.1 of Denis Serre's _Matrices_ as a reference.
-Thomas C
Consider the product of the negative unit matrix (which is negative definite) and the unit matrix (positive definite) (of the same size, of course). Both are Hermitian. Would not that mean, that the product should be positive definite? Maybe I am missing something? Christoph
On Mon, Mar 28, 2011 at 3:42 PM, Eugene Salamin <gene_salamin@yahoo.com> wrote:
Is this a theorem?
Let A and B be real symmetric matrices all of whose eigenvalues are positive. Then all eigenvalues of AB are positive.
-- Gene