Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site brl-tgr.ARPA Path: utzoo!linus!philabs!cmcl2!seismo!brl-tgr!gwyn From: gwyn@brl-tgr.ARPA (Doug Gwyn ) Newsgroups: net.math Subject: Re: Some Math problems Message-ID: <5437@brl-tgr.ARPA> Date: Tue, 23-Oct-84 21:47:42 EDT Article-I.D.: brl-tgr.5437 Posted: Tue Oct 23 21:47:42 1984 Date-Received: Fri, 26-Oct-84 06:46:34 EDT References: <689@ihuxt.UUCP> Organization: Ballistic Research Lab Lines: 28 > 2. Given a matrix A where > > > .68 -.6928 .24 0 > .6928 .5 -.52 0 > A = .24 .52 .82 0 > 0 0 0 1 > > find a transformation B such that BB=A. I don't have the solution right at hand, but here is how I would go about it (and its generalization) if it were my problem... First, note that the block diagonal form of A means you can limit your search to a block diagonal B: ? ? ? 0 B = ? ? ? 0 ? ? ? 0 0 0 0 1 This amounts to a 3-dimensional problem. Next, note that your matrix A is orthonormal. This means that it represents a 3-D rotation by some amount (call it theta) about some fixed axis. I would find the principal axes, and make up a solution B that represents a rotation of half-theta about the same axis. Books on linear algebra or crystallography will show you how to diagonalize the matrix.