Understanding Singular Vectors

A certain weighted average of the rows (and columns) of a non-negative matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular...

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Bibliographic Details
Published in:The College mathematics journal 2013-05, Vol.44 (3), p.220-226
Main Authors: James, David, Botteron, Cynthia
Format: Article
Language:English
Subjects:
Approximation
College Mathematics
Comparative politics
Data Analysis
Mathematical Concepts
Mathematical vectors
Mathematics Instruction
Matrices
Matrix
Set theory
Weighted averages
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Summary:A certain weighted average of the rows (and columns) of a non-negative matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular vectors that helps explain why the SVD is so effective in analyzing large data sets.
ISSN:0746-8342
1931-1346
DOI:10.4169/college.math.j.44.3.220