eig

Eigenvalues and eigenvectors.

Syntax

e       = eig(A)
[V, D]  = eig(A)
[V, D]  = eig(A, B)            % generalized: A*V = B*V*D
[V, D]  = eig(A, 'nobalance')

Description

With one output, returns the eigenvalues of A as a column vector. With two outputs, returns matrix V of eigenvectors and diagonal matrix D of eigenvalues such that A*V = V*D.

When A is detected to be Hermitian (or symmetric for real input), uses the symmetric eigensolver — guaranteed real eigenvalues and orthogonal eigenvectors. Otherwise uses the general eigensolver.

The two-matrix form solves the generalized eigenvalue problem: A*V = B*V*D. Pass 'nobalance' as the second argument to skip the balancing step (sometimes useful for matrices with widely-varying entries where balancing introduces numerical noise).

Examples

A = [2 0; 0 3];
eig(A)                   % [2; 3]
[V, D] = eig(magic(3));
norm(magic(3)*V - V*D)   % near-zero

See also

• svd — Singular value decomposition.
• hess — Hessenberg form of a matrix.
• schur — Schur decomposition.
• null — Orthonormal basis for the null space of a matrix.