From: Rory Niland <rniland@extro.ucc.usyd.edu.au>
Subject: Symmetric matrices
Date: Thu, 14 Oct 1999 18:35:58 -0700
Newsgroups: sci.math.num-analysis
Keywords: every square real matrix is the product of two symmetric ones

A.J.Bosch in the American Mathematical Monthly Vol 93 p.462 (1986)
proves that an arbitrary square real matrix can be factored into
two symmetric real matrices. This result has been known since Frobenius
(1910).
It is proved via the Jordan decomposition. It's new to me and I'd
like to know:
[1] given it is a simple result, does it have a simple proof?
[2] Can it be used to prove Jordan decomposition?
[3] Is it a unique factorization?
[4] Is it stable (unlike Jordan)?
[5] Numerical algorithm to do this - preferably avoiding Jordan.
[6] Geometrical interpretation. Easy to see an arbitrary matrix
	is the product of a symmetric and an orthogonal (by SVD).
[7] Any useful applications?

Any clues welcome!