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Reduction of a square matrix to triangular form

Published online by Cambridge University Press:  22 September 2016

F. Gerrish
F. Gerrish*
Affiliation:
Dept. of Mathematics, The Polytechnic, Kingston-on-Thames KT1 2EE
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Extract

Given a square matrix A with real or complex entries, there may not exist an invertible matrix S such that S-lAS is diagonal. For instance,

cannot be diagonalised in this way (the contrary assumption leads by easy direct calculation, to a contradition); however, this matrix is already upper-triangular.

Type
Research Article
Information
The Mathematical Gazette , Volume 64 , Issue 430 , December 1980 , pp. 266 - 270
Copyright
Copyright © Mathematical Association 1980

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References

1. Mirsky, L., An introduction to linear algebra, Oxford University Press (1955).Google Scholar
2. Archbold, J. W., Algebra (3rd edition), Pitman (1964).Google Scholar