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A Surprise from Geometry

by Ross Honsberger (University of Waterloo)

This article originally appeared in:
Mathematics Magazine
February, 1986

Subject classification(s): Algebra and Number Theory | Linear Algebra | Vector Spaces
Applicable Course(s): 3.8 Linear/Matrix Algebra

Consider \(n\) vectors issuing from the origin in \(n\)-dimensional space.  The author shows that the statement “any set of \(n\) vectors in \(n\)-space, no two of which meet at greater than right angles, can be rotated into the non-negative orthant” is true for \(n \leq 4\), but false for \(n>4\).

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Capsule Course Topic(s):
Linear Algebra | Geometry
Linear Algebra | Inner Product Spaces
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