How does matlabs eigs normalise eigenvectors?

In solving the generalised eigenvalue problem Ax=cBx using eig, one gets V and D as outputs where V is the eigenvectors corresponding to the eigenvalues contained in the main diagonal of D. My question is how does matlab normalise these eigenvectors?

In the case of the problem Ax=cx the documentation states 'The eigenvectors in V are normalized so that the 2-norm of each is 1' but for the generalised form 'The 2-norm of each eigenvector is not necessarily 1' (not helpful).

Answer 1

[Christine Tobler]

If the matrix B is symmetric positive definite, the eigenvectors are normalized in B-norm (and even orthogonal in B-norm if A is also symmetric). If B is not symmetric positive definite, the 2-norm of each eigenvector is 1, but they will not typically be orthonormal.

[Sam Tomlinson]

Brilliant, thank you very much!