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Eigencircles and associated surfaces

Published online by Cambridge University Press:  23 January 2015

M. J. Englefield  and
G.E. Farr
M. J. Englefield
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia
G.E. Farr
Affiliation:
Clayton School of Information Technology, Monash University, Clayton, Victoria 3800, Australia, e-mail: Graham.Farr@infotech.monash.edu.au
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Extract

Linear algebra has many fruitful connections with geometry. This article develops one such connection: the relationship between a 2 × 2 matrix and an associated circle which we call the eigencircle.

This connection was first investigated in a previous paper of ours [1], but the present paper is self-contained, and in fact introduces eigencircles in a different way. Here we discuss some surfaces containing the eigencircle which also have a number of interesting properties and connections with the associated matrix.

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 531 , November 2010 , pp. 438 - 449
Copyright
Copyright © The Mathematical Association 2010

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References

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