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)
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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 | Lucas Vieira |
| Other versions | Static version which inspired this animation and an extended version showing the effects of each column. |
Licensing
|
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:56, 17 September 2010 | | 400 × 330 (107 KB) | LucasVB | Shorter version (no intermediate per-column transforms). |
| 08:53, 8 September 2010 |  | 400 × 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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