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File:Singular value decomposition.gif

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Singular_value_decomposition.gif ‎(400 × 330 pixels, file size: 107 KB, MIME type: image/gif, looped, 45 frames, 36 s)

Summary

Description
English: Visual representation of a singular value decomposition of a 2-dimensional, real shearing M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M on the unit disc: it distorts the circle to an ellipse. The SVD decomposes M into three simple transformations: a rotation V*, a scaling Σ along the coordinate axes and a second rotation U. The SVD reveals the rotation of the ellipse with respect to the coordinate axes and the lengths σ1 resp. σ2 of the semi-major axis resp. semi-minor axis of the ellipse; they are just the singular values which occur as diagonal elements of the scaling Σ.
Date 08-09-2010
Source Own work
Author Kieff
Other versions

Static version which inspired this animation and an extended version showing the effects of each column.

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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File history

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Date/TimeThumbnailDimensionsUserComment
current16:56, 17 September 2010Thumbnail for version as of 16:56, 17 September 2010400 × 330 (107 KB)LucasVBShorter version (no intermediate per-column transforms).
08:53, 8 September 2010Thumbnail for version as of 08:53, 8 September 2010400 × 330 (155 KB)LucasVB{{Information |Description={{en|1=Animation depicting the various transformations performed for each column of each matrix in the singular value decomposition.}} |Source={{own}} |Author=Kieff |Date=08-09-2010 |Permission= |other_versions=St
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