hess

Hessenberg form of matrix

Syntax

H = hess(A)
[P,H] = hess(A)
[AA,BB,Q,Z] = hess(A,B)


Description

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.

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

More About

Hessenberg Matrix

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

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 contains only NaN values.

• Code generation does not support sparse matrix inputs for this function.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a