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Cyclic Transformations of Polygons and the Generalized Inverse

Published online by Cambridge University Press:  20 November 2018

Philip J. Davis*
Affiliation:
Brown University, Providence, Rhode Island
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By a polygon with n vertices (an n-gon) we shall mean an ordered n-tuple of complex numbers (z 1, z 2, … , zn ). The numbers zi will be called the vertices of the polygon. The zi may or may not be distinct, and it shall not matter whether a “conventional” polygon can be drawn with the zi as vertices. We shall operate in the spirit of the book of Bachmann and Schmidt [2] though not at the same level of algebraic generality inasmuch as these authors allow zi to belong to a general field.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Ahlberg, J. H., Block circulants of level K, Division of Applied Mathematics, Brown University, Prov. R.I., June, 1976.Google Scholar
2. Bachmann, F. and Schmidt, E., n-gons, Translated by Garner, C. W. L., Mathematical Exposition No. 18 (Univ. of Toronto Press, Toronto, 1975).CrossRefGoogle Scholar
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7. Drazin, M. P., Pseudo inverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506514.Google Scholar
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10. Schoenberg, I. J., The finite Fourier series and elementary geometry, Amer. Math. Monthly 57 (1950), 390404.Google Scholar
11. Trapp, G. E., Inverses of circulant matrices and block circulant matrices, Kyungpook Math. Jour. 13 (1973), 1120.Google Scholar
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