## MathGenie

# eig

Eigenvalues and eigenvectors

### Syntax and Description

eig(A) | returns diagonal matrix D of eigenvalues, matrix V whose columns are the corresponding right eigenvectors, so that A*V = V*D and the full matrix W whose columns are the corresponding left eigenvectors, so that W'*A = D*W'. The eigenvalue problem is to determine the solution to the equation Av = λv, where A is an n-by-n matrix, v is a column vector of length n, and λ is a scalar. The values of λ that satisfy the equation are the eigenvalues. The corresponding values of v that satisfy the equation are the right eigenvectors. The left eigenvectors, w, satisfy the equation w'A = λw'. |