How does matlabs eigs normalise eigenvectors?

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Sam Tomlinson
Sam Tomlinson 2018-3-2
评论： Sam Tomlinson 2018-3-5
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).

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Christine Tobler
Christine Tobler 2018-3-2
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.

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