Schur Decomposition of a Matrix --- Generic Function
DESCRIPTION:
Computes the Schur decomposition (including eigenvalues) of a square matrix.
In S-PLUS, only one class has a method for this function -- the
"Matrix" class from the Matrix library. It is defined as a method to
allow users to easily incorporate customized versions into S-PLUS.
USAGE:
schur(x, ...)
REQUIRED ARGUMENTS:
x:
a square matrix. No missing values or IEEE special values are allowed.
OPTIONAL ARGUMENTS:
...:
most methods will have additional arguments, for example an argument
indicating whether or not to compute the Schur vectors.
VALUE:
a representation of all or part of the Schur decomposition of x.
BACKGROUND:
If A is a square matrix, then A = Q T t(Q), where Q is orthogonal, and
T is upper quasi-triangular (nearly triangular with either 1 by 1 or 2 by 2
blocks on the diagonal). The eigenvalues of A are the same as those of 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.
REFERENCES:
Golub, G., and Van Loan, C. F. (1989).
Matrix Computations,
2nd edition, Johns Hopkins, Baltimore.