文件:Singular-Value-Decomposition.svg.png

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.