文件:Singular-Value-Decomposition.svg.png

Illustration of the singular value decomposition [math]\displaystyle{ UΣV^⁎ }[/math] of a real 2 × 2 matrix [math]\displaystyle{ M }[/math].

Top: The action of [math]\displaystyle{ M }[/math], indicated by its effect on the unit disc D and the two canonical unit vectors [math]\displaystyle{ e_1 }[/math] and [math]\displaystyle{ e_2 }[/math].

Left: The action of [math]\displaystyle{ V^⁎ }[/math], a rotation, on D, [math]\displaystyle{ e_1 }[/math], and [math]\displaystyle{ e_2 }[/math].

Bottom: The action of [math]\displaystyle{ Σ }[/math], a scaling by the singular values [math]\displaystyle{ σ_1 }[/math] horizontally and [math]\displaystyle{ σ_2 }[/math] vertically.

Right: The action of [math]\displaystyle{ U }[/math], another rotation.