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eigen(x [,maxit:N, nonconvok:T]), x a REAL symmetric matrix with no
  MISSING values, integer N > 0

Keywords: matrix algebra
eigen(x) computes an eigenvector/eigenvalue decomposition of the
REAL symmetric matrix x.  The result is a structure with two REAL
components, 'values' and 'vectors'.  It an error if x contains any
MISSING values.

Vector eigen(x)$values contains the eigenvalues in decreasing order
(eigen$values[i] >= eigen$values[i+1]).  If all you need are the eigen-
values, use eigenvals(x).

The columns of square matrix eigen(x)$vectors are the eigenvectors of x
with eigen$vectors[,j] corresponding to eigen$values[j].  The eigen-
vectors are orthonormal, even when there are repeated eigenvalues.

From the properties of the eigenvalue/eigenvector decomposition of a
  eigen(x)$vectors %*% dmat(eigen(x)$values) %*% eigen(x)$vectors'
should be the same as x, except for rounding error.

It is possible for the algorithm used by eigen() not to converge,
although it rarely happens.  When it happens, the message
  ERROR: algorithm to compute eigenvalues in eigen() did not converge
is printed.  Keywords 'maxit' and 'nonconvok' may be helpful in this

eigen(x maxit:N), where N > 0 is an integer, computes the eigenvalues
and eigenvectors, but sets the maximum number of iterations in the
algorithm to N.  The default value is 30.  By using N > 30, this may
allow you to compute eigenvalues and vectors you can't otherwise

eigen(x [,maxit:N] ,nonconvok:T) does the same, except failure to
converge is not an error.  When convergence does not occur, no message
printed and NULL is returned.  You can use this in a macro to make it
possible to recover from failure to converge, perhaps by invoking
eigen() again using 'maxit' to increase the number of iterations.

Keyword phrases 'maxit:T' and 'nonconvok:T' may also be used on
eigenvals(), releigen() and releigenvals().

See also eigenvals(), trideigen(), releigen(), and releigenvals().

Gary Oehlert 2003-01-15