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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Singular Value Decomposition (SVD) and Polar Form
verfasst von : Jean Gallier
Erschienen in: Geometric Methods and Applications
Verlag: Springer New York
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In this section we assume that we are dealing with a real Euclidean space
E
. Let
$$ f : E \rightarrow E $$
be any linear map. In general, it may not be possible to diagonalize
f
. We show that every linear map can be diagonalized if we are willing to use
two
orthonormal bases. This is the celebrated
singular value decomposition (SVD)
. A close cousin of the SVD is the
polar form
of a linear map, which shows how a linear map can be decomposed into its purely rotational component (perhaps with a flip) and its purely stretching part.