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An Argand diagram for two by two matrices

Published online by Cambridge University Press:  01 August 2016

Tony Crilly
Tony Crilly*
Affiliation:
Middlesex Business School, The Burroughs, Hendon, London NW4 4BT, e-mail: t.crilly@mdx.ac.uk
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Extract

A vivid memory of mine is of being shown that certain 2 × 2 matrices were ‘really’ complex numbers. The correspondence between matrices of the form

and complex numbers

seemed magical and the additional remark that

was an unexpected bonus. The correspondence has been examined in various articles in the Gazette [1, 2]. That it is an isomorphism is seen by comparing

with

in the case of addition, and, in the case of multiplication, by comparing

with

Type
Articles
Information
The Mathematical Gazette , Volume 87 , Issue 509 , July 2003 , pp. 209 - 216
Copyright
Copyright © The Mathematical Association 2003

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References

1. Gerrish, Frank Ordered Pairs, Math. Gaz. 79 (March 1995) pp. 30–46.Google Scholar
2. Quadling, Douglas Q is for Quaternions, Math. Gaz. 63 (June 1979) pp. 98–110.Google Scholar
3. Clifford, William K. A preliminary sketch of biquaternions, Proc. London Math. Soc., 4 (1873) pp. 381–395. Also Coll. Papers, (Reprint: 1968) pp. 181–200.Google Scholar
4. Van der Waerden, B. A history of algebra, Springer (1985).Google Scholar
5. Rosenfel’d, B. A. tr.Shenitzer, A. A history of non-Euclidean geometry, Springer (1988).Google Scholar