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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    -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

See Also

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