11471
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Image Compression via the Singular Value Decomposition
Chris Maes
Numerical Instability in the Gram-Schmidt Algorithm
Chris Boucher
Brauer's Cassini Ovals versus Gershgorin Circles
Ludwig Weingarten
Numerical Range for Some Complex Upper Triangular Matrices
Ludwig Weingarten
Maximum Absolute Column Sum Norm
Eugenio Bravo Sevilla
Enclosing the Spectrum by Gershgorin-Type Sets
Ludwig Weingarten
Gershgorin Circles
Chris Maes
Image Compression via the Fourier Transform
Chris Maes
Three Parametrizations of Rotations
Aaron T. Becker and Benedict Isichei
QR Decomposition
Chris Boucher
Related Topics
Algorithms
Ellipses
Linear Algebra
Numerical Analysis
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+