**Rotation, Scaling, Rotation**

In the special but common case in which M is just an *m×m* square matrix with positive determinant whose entries are plain real numbers, then U, V*, and Σ are *m×m* matrices of real numbers as well, Σ can be regarded as a scaling matrix, and U and V* can be viewed as rotation matrices.

If the abovementioned conditions are met, the expression can thus be intuitively interpreted as a composition (or sequence) of three geometrical transformations: a rotation, a scaling, and another rotation. For instance, the figure above explains how a shear matrix can be described as such a sequence.

Read more about this topic: Singular Value Decomposition, Intuitive Interpretations

### Other articles related to "rotations, rotation":

... is a form of stereoisomerism in which the isomers can be interconverted exclusively by

**rotations**about formally single bonds ... isomers or conformers and specifically as rotamers when the

**rotation**leading to different conformations is restricted (hindered)

**rotation**, in the sense ... The rotational barrier, or barrier to

**rotation**, is the activation energy required to interconvert rotamers ...

... Formally, a

**rotation**system is defined as a pair (σ,θ) where σ and θ are permutations acting on the same ground set B, θ is a fixed-point-free involution, and the group ... To derive a

**rotation**system from a 2-cell embedding of a connected multigraph G on an oriented surface, let B consist of the darts (or flags, or half-edges) of G that is, for each edge of G we ... on an orientable but not oriented surface, it generally corresponds to two

**rotation**systems, one for each of the two orientations of the surface ...

... Rotation, usually called spin, plays a role in many sports ... Topspin and backspin in tennis ...

... These two spectrographs are able to rotate to compensate for the

**rotation**of the image caused by the use of a heliostat ... equipped with a static optical table with no image

**rotation**correction and is therefore rarely used ... can only be used for imaging on static optical tables and do not provide image

**rotation**correction ...

... A detent is a device used to mechanically resist or arrest the

**rotation**of a wheel, axle, or spindle ... Detents are for example used to simply arrest

**rotation**in one direction or to intentionally divide a

**rotation**into discrete increments ...

### Famous quotes containing the word rotation:

“The lazy manage to keep up with the earth’s *rotation* just as well as the industrious.”

—Mason Cooley (b. 1927)