I'm not seeing where it says that; in fact, the article you cite seems to go out of its way *not* to say that. It says that if M and N are positive definite, then MNM and NMN are also, and that if M and N commute, then MN is positive definite. Surely if the general theorem were true, they would have said it, rather than presenting these weaker results. On Mon, Mar 28, 2011 at 4:17 PM, quad <quad@symbo1ics.com> wrote:
In simplest terms, the product of two positive definite-matrices is positive-definite.
See http://en.wikipedia.org/wiki/Positive-definite_matrix
-Robert
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
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
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