Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T13:50:54.875Z Has data issue: false hasContentIssue false
  • English
  • Français

Cyclic Transformations of Polygons and the Generalized Inverse

Published online by Cambridge University Press:  20 November 2018

Philip J. Davis
Philip J. Davis*
Affiliation:
Brown University, Providence, Rhode Island
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By a polygon with n vertices (an n-gon) we shall mean an ordered n-tuple of complex numbers (z1, z2, … , 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
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 756 - 770
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).Google Scholar
3. Ben-Israel, A. and Greville, T. N. E., Generalized inverses (Academic Press, N.Y., 1974).Google Scholar
4. Choquet, G., Geometry in a modern setting (London, 1969).Google Scholar
5. Coxeter, H. S. M., Introduction to geometry (Wiley, N. Y., 1969).Google Scholar
6. Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited (Mathematical Association of America, 1975).Google Scholar
7. Drazin, M. P., Pseudo inverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514.Google Scholar
8. Englefield, M. J., The commuting inverses of a square matrix, Proc. Camb. Phil. Soc. 62 (1966), 667–671.Google Scholar
9. Erdelyi, I., On the matrix equation Ax = \Bx, J. Math. Anal. Appl. 17 (1967), 119–132.Google Scholar
10. Schoenberg, I. J., The finite Fourier series and elementary geometry, Amer. Math. Monthly 57 (1950), 390–404.Google Scholar
11. Trapp, G. E., Inverses of circulant matrices and block circulant matrices, Kyungpook Math. Jour. 13 (1973), 11–20.Google Scholar