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Quadratic forms associated with planar endomorphisms

Published online by Cambridge University Press:  17 April 2009

G. E. Prince
G. E. Prince
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Vic. 3083, Australia e-mail: [email protected]
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Abstract

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Any linear operator A on 2 is shown to have two real quadratic form on S1 associated with it. They represent the expansion and rotation of the map and the eigenvalues of A can be described in a geometrically intrinsic way in therms of the eigenvalues of these two quadratic forms via the formula .

A number of theorems concerning these quadṙatic forms are presented.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 459 - 465
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Prince, G. and Stathopoulos, G. ‘The geometry of planar flows’, (preprint, Department of Mathematics, La Trobe University, 1999). Available at http://www.latrobe.edu.au/www/mathstats/Staff/prince.html.Google Scholar
[2]Stathopoulos, G., Geometry of planar flows, (M.Sc. Thesis) (Department of Mathematics, La Trobe University, 1998).Google Scholar
[3]Truesdell, C., A first course in rational continuum mechanicas, Pure and Applied Mathematics 71 (Academic Press, Boston, MA, 1977).Google Scholar