Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T20:29:11.522Z Has data issue: false hasContentIssue false

Symmetry, graphs and eigenvalues

Published online by Cambridge University Press:  22 September 2016

J. V. Greenman*
Affiliation:
Department of Mathematics, University of Essex, Colchester CO4 3SQ

Extract

The discussion of symmetry in modern mathematics syllabuses can be taken a stage further in the sixth form to show how symmetry can often be used to simplify the solution of certain types of problems. This article gives just one example, that of determining the eigenvalues and eigenvectors of an n × n matrix. The theory involves two steps. In the first we show how the eigenvalues of a matrix M can under certain circumstances be found from those of a commuting matrix P. In the second step we show how to construct, from the symmetry properties of matrix M, commuting matrices P whose eigenvalues are readily found.

Type
Research Article
Copyright
Copyright © Mathematical Association 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Greenman, J. V., Graphs and determinants, Mathl Gaz. 60, 241246 (No. 414, December 1976).CrossRefGoogle Scholar
1. Greenman, J. V., Graphs and determinants, Mathl Gaz. 60, 241246 (No. 414, December 1976).CrossRefGoogle Scholar
2. Greenman, J. V., Graphs and Markov chains, Mathl Gaz. 61, 4954 (No. 415, March 1977).CrossRefGoogle Scholar
3. Feynman, R. P., Leighton, R. B. and Sands, M. L., The Feynman lectures on physics, Vol. 3. Addison-Wesley (1965).Google Scholar
4. Rouvray, D. H., The search for useful topological indices in chemistry, Am. Scient. 61, 729735 (1973).Google Scholar