From: "Andrew Baker" To: lssiu@hkusua.hku.hk Date: Fri, 17 Dec 1999 14:17:55 +0000 Subject: Re: topology over real closed fields Dear Lok-Shun Siu, I was interested in your questions since I recently published a proof of the existence of quaternionic eigenvalues using the Lefschetz Fixed Point Theorem [Right eigenvalues for quaternionic matrices: a topological approach, Linear Algebra and its Applications, 286 (1999), 303-9; see also http://www.maths.gla.ac.uk/~ajb/dvi-ps.html] I referred to a survey paper by Zhang [Quaternions and matrices of quaternions, Linear Algebra and its Applications, 251 (1997), 21--57] which I think has a more algebraic proof that probably works over any formally real field. Andy Baker Dr A.J. Baker, Department of Mathematics, University of Glasgow, G12 8QW, Scotland. email a.baker@maths.gla.ac.uk WWW http://www.maths.gla.ac.uk/~ajb tel. (0141) 339 8855 ext. 6140 fax (0141) 330 4111