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MathGroup Archive 2005

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does a matrix equivalent of the Arg function exist?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53585] does a matrix equivalent of the Arg function exist?
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Wed, 19 Jan 2005 01:59:41 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Arg[x+I*y] exists for any complex number.
The 2by2 Matrix:
{{x,-y},{y,x}}
behaves very much like the complex number.
With Euler matrices being three rotations by angles such that a total 
angle exists,
it seems that an angle equivalency function like Arg should exist
generally for nbyn matrices as a kind of measure like the determinant.
Has anyone heard of such a matrix measure?
Any ideas about how to form such a function?
It would be useful geometrically in things like space and point groups 
used in
crystalography and spectra of molecules.
-- 
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 
619-5610814 :
alternative email: rlbtftn at netscape.net
URL :  http://home.earthlink.net/~tftn


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