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The SVD decomposes M into three simple transformations: a Rotation matrix | rotation V < sup >*</ sup >, a Scaling matrix | scaling Σ along the rotated coordinate axes and a second rotation U. The lengths σ < sub > 1 </ sub > and σ < sub > 2 </ sub > of the Ellipse # Elements of an ellipse | semi-axes of the ellipse are the singular value s of M.

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The SVD decomposes M into three simple transformations: a Rotation matrix | rotation V < sup >*</ sup >, a scaling ( geometry ) | scaling Σ along the rotated coordinate axes and a second rotation U. Σ is a diagonal matrix containing in its diagonal the singular values of M, which represent the lengths σ < sub > 1 </ sub > and σ < sub > 2 </ sub > of the Ellipse # Elements of an ellipse | semi-axes of the ellipse.

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