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Singular Value Decomposition
The singular value decomposition is a factorization of a matrix
into
. A vector
is first rotated by an angle β via
, then
is scaled by a diagonal matrix
to form
. Finally the vector
is rotated by an angle ω to form
.
Contributed by:
Chris Maes
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Note that U and V are orthogonal matrices and thus do not alter the length of the vectors. In 2D the diagonal matrix Σ has the form
here
are the singular values of the matrix.
RELATED LINKS
Singular Value Decomposition
(
Wolfram
MathWorld
)
Orthogonal Matrix
(
Wolfram
MathWorld
)
Rotation Matrix
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Singular Value Decomposition
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/SingularValueDecomposition/
Contributed by:
Chris Maes
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