Hessenberg form of matrix
H = hess(A)
[P,H] = hess(A)
[AA,BB,Q,Z] = hess(A,B)
H = hess(A) finds
the Hessenberg form of matrix
[P,H] = hess(A) produces
a Hessenberg matrix
H and a unitary matrix
A = P*H*P' and
P'*P = eye(size(A)) .
[AA,BB,Q,Z] = hess(A,B) for
an upper Hessenberg matrix
AA, an upper triangular
BB, and unitary matrices
Q*A*Z = AA and
Q*B*Z = BB.
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
A Hessenberg matrix contains zeros below the first subdiagonal. If the matrix is symmetric or Hermitian, then the form is tridiagonal. This matrix has the same eigenvalues as the original, but less computation is needed to reveal them.
Usage notes and limitations:
Generated code can return a different Hessenberg decomposition than MATLAB® returns.
When the input matrix contains a nonfinite value, the generated code output
Code generation does not support sparse matrix inputs for this function.
backgroundPoolor accelerate code with Parallel Computing Toolbox™
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.