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View of /pkg/man/Schur.Rd

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Revision 686 - (download) (as text) (annotate)
Thu Mar 31 21:19:35 2005 UTC (14 years, 3 months ago) by bates
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Create "fallback" methods for any kind of numeric, dense matrix
\title{Schur Decomposition of a Matrix}
Schur(x, vectors, \dots)
    Computes the Schur decomposition and eigenvalues of a square matrix.
    numeric or complex square Matrix inheriting from class
    \code{"Matrix"}. Missing values (NAs) are not allowed.
  \item{vectors}{logical.  When \code{TRUE} (the default), the Schur
    vectors are computed.
  \item{\dots}{further arguments passed to or from other methods.}      
  An object of class \code{c("schur.Matrix", "decomp")} whose
  attributes include the eigenvalues, the Schur quasi-triangular form
  of the matrix, and the Schur vectors (if requested).
  Based on the Lapack functions \code{dgeesx}
  If \code{A} is a square matrix, then \code{A = Q T t(Q)}, where
  \code{Q} is orthogonal, and \code{T} is upper quasi-triangular
  (nearly triangular with either 1 by 1 or 2 by 2 blocks on the
  The eigenvalues of \code{A} are the same as those of \code{T},
  which are easy to compute. The Schur form is used most often for
  computing non-symmetric eigenvalue decompositions, and for computing
  functions of matrices such as matrix exponentials.
  Anderson, E., et al. (1994).
  \emph{LAPACK User's Guide,}
  2nd edition, SIAM, Philadelphia.
Schur(Hilbert(9))              # Schur factorization (real eigenvalues)
A <- Matrix(rnorm( 9*9, sd = 100), nrow = 9)
schur.A <- Schur(A)
#mod.eig <- Mod(schur.A$values) # eigenvalue modulus
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