MAKE A MEME View Large Image Singular value decomposition.gif 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 ...
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Keywords: Singular value decomposition.gif 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<sup> </sup> a scaling 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 <sub>1</sub> resp <sub>2</sub> 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 own Kieff 08-09-2010 Static version which inspired this animation and an extended version showing the effects of each column Linear algebra Mathematical animations Animated diagrams
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