Singular Value Decomposition - Intuitive Interpretations - Rotation, Scaling, Rotation

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

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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)