MATLAB Function Reference Volume 1: A - E - Bad Request

eig
2-470
[V,D] = eig(A,B) produces a diagonal matrix D of generalized eigenvalues
and a full matrix V whose columns are the corresponding eigenvectors so that
A*V = B*V*D.
[V,D] = eig(A,B,flag) specifies the algorithm used to compute eigenvalues
and eigenvectors. flag can be:
'chol' Computes the generalized eigenvalues of A and B using the
Cholesky factorization of B. This is the default for symmetric
(Hermitian) A and symmetric (Hermitian) positive definite B.
'qz' Ignores the symmetry, if any, and uses the QZ algorithm as it
would for nonsymmetric (non-Hermitian) A and B.
Remarks The eigenvalue problem is to determine the nontrivial solutions of the equation
Ax = λx
where A is an n-by-n matrix, x is a length n column vector, and λ is a scalar.
The n values of λ that satisfy the equation are the eigenvalues, and the
corresponding values of x are the right eigenvectors. In MATLAB, the function
eig solves for the eigenvalues λ , and optionally the eigenvectors x .
The generalized eigenvalue problem is to determine the nontrivial solutions of
the equation
Ax = λBx
where both A and B are n-by-n matrices and λ is a scalar. The values of λ that
satisfy the equation are the generalized eigenvalues and the corresponding
values of x are the generalized right eigenvectors.
If B is nonsingular, the problem could be solved by reducing it to a standard
eigenvalue problem
B 1 – Ax = λx
Because B
can be singular, an alternative algorithm, called the QZ method, is
necessary.
When a matrix has no repeated eigenvalues, the eigenvectors are always
independent and the eigenvector matrix V diagonalizes the original matrix A if
applied as a similarity transformation. However, if a matrix has repeated