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A Surprise from Geometry

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 \(n>4\).

Old Node ID: 
3374
MSC Codes: 
15A03
Author(s): 
Ross Honsberger (University of Waterloo)
Publication Date: 
Friday, February 5, 2010
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
February, 1986
Subject(s): 
Algebra and Number Theory
Linear Algebra
Vector Spaces
Topic(s): 
Linear Algebra
Geometry
Inner Product Spaces
Flag for Digital Object Identifier: 
Digital Object Identifier: 
10.4169/capsules003374
Publish Page: 
Furnished by JSTOR: 
Rating Count: 
29.00
Rating Sum: 
83.00
Rating Average: 
2.86
Applicable Course(s): 
3.8 Linear/Matrix Algebra
Modify Date: 
Friday, February 5, 2010
Average: 2.9 (29 votes)

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