Hessenberg form of matrix
H = hess(A)
[P,H] = hess(A)
[AA,BB,Q,Z] = hess(A,B)
H = hess(A) finds H,
the Hessenberg form of matrix A.
[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.
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.
H is a 3-by-3 eigenvalue test matrix:
H =
-149 -50 -154
537 180 546
-27 -9 -25Its 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