what is the normalizings in generalized eigvalues in matlab

Hi All,

In matlab, i used

[V, D]=eig(A, B)

then the eigenvectors V can be obtained? but what is the normalizing of V used in matlab.

For example, if i used [v, d]=eig(A), then the the column of v is normalized to be a unit vector.

Thanks.

Answer 1

[Andrew Newell]

The documentation for eig says that the vectors are not normalized.

EDIT: QZ factorization for generalized eigenvalues gives more detail on how the generalized eigenvalues are obtained. As for how this decomposition works, you could look at this section of Golub and Van Loan's classic book.

[David Zhang]

NO, eig(A) will output the unit eigenvector, but i dont know eig(A, B) will output what kind of eigenvector? because only n-1 independent equation cant not solve n variables uniquely, and one of them must be assumed to provide the user the eigenvectors?thanks

[David Zhang]

Note For eig(A), the eigenvectors are scaled so that the norm of each is 1.0. For eig(A,B), eig(A,'nobalance'), and eig(A,B,flag), the eigenvectors are not normalized.

Also note that if A is symmetric, eig(A,'nobalance') ignores the nobalance option since A is already balanced.

If eig(A, B) are not normalized, so how it give the value of one variable firstly? thanks