eig

Eigenvalues and eigenvectors.

Syntax

• e = eig(A)
• [V, D] = eig(A)
• e = eig(A, balanceOption)
• [V, D] = eig(A, balanceOption)
• e = eig(A, B)
• [V, D] = eig(A, B)
• e = eig(A, B, balanceOption)
• [V, D] = eig(A, B, balanceOption)

Input argument

• A - a numeric value: scalar or square matrix (double or single, complex or real)
• B - a numeric value: scalar or square matrix (double or single, complex or real)
• balanceOption - a string: 'nobalance' (disable preliminary balancing) or 'balance' (default).

Output argument

• e - real or complex number (double or single), Eigenvalues (returned as column vector).
• V - real or complex number (double or single), square right eigenvectors.
• D - real or complex number (double or single), Eigenvalues (returned as diagonal matrix).

Description

eig(A) returns the Eigenvalues and eigenvectors.

eig(A, B) returns the generalized Eigenvalues and eigenvectors.

Bibliography

[1] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK User's Guide (http://www.netlib.org/lapack/lug/ lapack_lug.html), Third Edition, SIAM, Philadelphia, 1999.

Examples

A = [10 -20 40; -50 20 0; 10 0 30]
e = eig(A)
[V, D] = eig(A)

A = [1/sqrt(2) 0; 0 1];
B = [0 1; -1/sqrt(2) 0];
[V, D] = eig(A, B)

See also

svd, schur.

History

Author

Allan CORNET