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  yourself.
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  yourself.
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  Computing the eigenvectors is the slow part for large matrices.
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  Computing the eigenvectors is the slow part for large matrices.
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  Computing the eigendecomposition of a matrix is subject to errors on a
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  Computing the eigendecomposition of a matrix is subject to errors on a
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  real-world computer: the definitive analysis is Wilkinson (1965).  All
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  real-world computer: the definitive analysis is \bibcitet{R:Wilkinson:1965}.  All
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  you can hope for is a solution to a problem suitably close to
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  you can hope for is a solution to a problem suitably close to
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  \code{x}.  So even though a real asymmetric \code{x} may have an
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  \code{x}.  So even though a real asymmetric \code{x} may have an
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  algebraic solution with repeated real eigenvalues, the computed
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  algebraic solution with repeated real eigenvalues, the computed
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  solution may be of a similar matrix with complex conjugate pairs of
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  solution may be of a similar matrix with complex conjugate pairs of
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  eigenvalues.
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  eigenvalues.
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  LAPACK is from \url{https://netlib.org/lapack/} and its guide is listed
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  LAPACK is from \url{https://netlib.org/lapack/} and its guide is listed
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  in the references.
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  in the references.
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}
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}
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\references{
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\references{
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  \bibshow{R:Anderson+Bai+Bischof:1999,
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  \bibshow{R:Anderson+Bai+Bischof:1999,
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    R:Becker+Chambers+Wilks:1988}
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    R:Becker+Chambers+Wilks:1988,
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  Wilkinson, J. H. (1965) \emph{The Algebraic Eigenvalue Problem.}
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  Clarendon Press, Oxford.
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    R:Wilkinson:1965}
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}
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}
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\seealso{
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\seealso{
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  \code{\link{svd}}, a generalization of \code{eigen}; \code{\link{qr}}, and
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  \code{\link{svd}}, a generalization of \code{eigen}; \code{\link{qr}}, and
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  \code{\link{chol}} for related decompositions.
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  \code{\link{chol}} for related decompositions.