The invariant straight lines of an affine transformation in ℝ^n without fixed points

Erwin Kasparek

Published: 2010-09-30

Vol. 24 (2010)

The invariant straight lines of an affine transformation in ℝ^n without fixed points

Erwin Kasparek

Abstract

In this note we prove that every affine transformation in ℝⁿ of the form f(x) = Ax+a without fixed points has an invariant straight line if and only if when g(a)∈Im(g◦g), where g(x) = (A−I)x.

Keywords:

affine transformation , invariant affine subspace

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Kasparek, E. (2010). The invariant straight lines of an affine transformation in ℝ^n without fixed points. Annales Mathematicae Silesianae, 24, 35–37. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14033

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Vol. 24 (2010)
Published: 2010-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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