Eigencircles and associated surfaces

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 sel...

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Bibliographic Details
Published in:Mathematical gazette 2010-11, Vol.94 (531), p.438-449
Main Authors: ENGLEFIELD, M. J., FARR, G. E.
Format: Article
Language:English
Subjects:
Circles
Discriminants
Eigenvalues
Eigenvectors
Geometric planes
Hyperboloids
Mathematical vectors
Matrices
Quaternions
Tangents
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Summary: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.
ISSN:0025-5572
2056-6328
DOI:10.1017/S002555720000173X