Figure Properties - SERC

hess
2hess
Purpose Hessenberg form of a matrix
Syntax [P,H] = hess(A)
H = hess(A)
[AA,BB,Q,Z] = HESS(A,B)
Description H = hess(A) finds H, the Hessenberg form of matrix A.
2-1060
[P,H] = hess(A) produces a Hessenberg matrix H and a unitary matrix P so
that A = P*H*P' and P'*P = eye(size(A)).
[AA,BB,Q,Z] = HESS(A,B) for square matrices A and B, produces an upper
Hessenberg matrix AA, an upper triangular matrix BB, and unitary matrices Q
and Z such that Q*A*Z = AA and Q*B*Z = BB.
Definition A Hessenberg matrix is zero below the first subdiagonal. If the matrix is
symmetric or Hermitian, the form is tridiagonal. This matrix has the same
eigenvalues as the original, but less computation is needed to reveal them.
Examples H is a 3-by-3 eigenvalue test matrix:
H =
-149 -50 -154
537 180 546
-27 -9 -25
Its Hessenberg form introduces a single zero in the (3,1) position:
hess(H) =
-149.0000 42.2037 -156.3165
-537.6783 152.5511 -554.9272
0 0.0728 2.4489
Algorithm Inputs of Type Double
For inputs of type double, hess uses the following LAPACK routines to
compute the Hessenberg form of a matrix: