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The Procrustes Problem

The Procrustes problem (see [158]) is the minimization of
for constant and over the manifold .
This minimization determines the nearest matrix to for
which

i.e. the columns of span an invariant subspace of .
The differential of
is given by

This can be derived following the process outlined above.
Observe that

The second derivative of is given by the equation

where
,
which can be obtained by varying the expression for .

Susan Blackford
2000-11-20