Purpose

LA_GEEV computes for a real or complex square matrix $A$, the eigenvalues and, optionally, the left and/or right eigenvectors. A right eigenvector $v_j$ of $A$ satisfies

$$A \, v_j = \lambda_j \, v_j$$

where $\lambda_j$ is its eigenvalue. A left eigenvector $u_j$ of $A$ satisfies

$$u_j^H \, A = \lambda_j \, u_j^H$$

where $u_j^H$ denotes the conjugate-transpose of $u_j$.