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On Some Symmetric Sets of Unit Vectors

by Murray S. Klamkin (University of Alberta, Canada)

This article originally appeared in:
Mathematics Magazine
October, 1991

Subject classification(s): Algebra and Number Theory | Linear Algebra | Vector Spaces
Applicable Course(s): 3.8 Linear/Matrix Algebra | 4.21 Senior Seminar / Independent Study in Math

Given symmetric unit vectors \(u_i\), conditions on real numbers \(x_i\) are considered to be able to conclude that \(\sum x_i u_i \Rightarrow x_i = 0\) for all \(i\). Different kinds of “symmetry” lead to different conclusions.

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Capsule Course Topic(s):
Linear Algebra | Vector Spaces, Subspaces
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