hess

Hessenberg form of a matrix.

Syntax

H              = hess(A)
[P, H]         = hess(A)
[P, H, Q, Z]   = hess(A, B)        % generalized

Description

Reduces A to upper-Hessenberg form H (zeros below the first subdiagonal) via an orthogonal similarity transformation. With two outputs, also returns the orthogonal P such that A = P*H*P'.

The two-matrix form computes the generalized Hessenberg reduction: A = P*H*Q' and B = P*T*Z' where H is upper-Hessenberg and T is upper-triangular. Used as a preprocessing step in eigenvalue computations.

Examples

[P, H] = hess(magic(4));
norm(P*H*P' - magic(4))  % near-zero

See also

• eig — Eigenvalues and eigenvectors.
• schur — Schur decomposition.
• qr — QR decomposition.