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Illustration of the singular value decomposition UΣV⁎ of a real 2 × 2 matrix M.
Top: The action of M, indicated by its effect on the unit disc D and the two canonical unit vectors e1 and e2.
Left: The action of V⁎, a rotation, on D, e1, and e2.
Bottom: The action of Σ, a scaling by the singular values σ1 horizontally and σ2 vertically.
Right: The action of U, another rotation.