next up previous contents index Next: Singular Value
Decomposition Up: Nonsymmetric Eigenproblems Previous:
Nonsymmetric Eigenproblems  Eigenvalues, Eigenvectors, and Schur
Factorization    Let A be a square n-by-n matrix. A scalar
tex2html_wrap_inline12778 is called an eigenvalue  and a nonzero
column vector v the corresponding right eigenvector  if
tex2html_wrap_inline13982. A nonzero column vector u satisfying
tex2html_wrap_inline13986 is called the left eigenvector . The
first basic task of the routines described in this section is to
compute, for a given matrix A, all n values of
tex2html_wrap_inline12778 and, if desired, their associated
right eigenvectors v and/or left eigenvectors u.  A second basic
task is to compute the Schur factorization of a matrix A.   If A
is complex, then its Schur factorization is
tex2html_wrap_inline14002, where Z is unitary and T is upper
triangular. If A is real, its Schur factorization is
tex2html_wrap_inline14010, where Z is orthogonal, and T is upper
quasi-triangular (1