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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