# Is the generalized eigenvalue problem only for square matrices?

From Wikipedia:

A generalized eigenvalue problem (2nd sense) is the problem of finding a vector v that obeys $$A\mathbf{v} = \lambda B \mathbf{v} \quad \quad$$ where $A$ and $B$ are matrices.

I was wondering if $A$ and $B$ are required to be square matrices? The definition doesn't seem to require this, but the next sentence does

The possible values of $λ$ must obey the following equation $$\det(A - \lambda B)=0.\,$$

Thanks!

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Well, also regular eigenvectors are defined for square matrices, otherwise things may hardly make sense (exercise: try with a $\,2\times 3\,$ matrix...) – DonAntonio Nov 25 '12 at 2:43
Regular ones do, but the definition for generalized ones seems not. – Tim Nov 25 '12 at 2:47
Well it seems yes, at least according to Wiki... – DonAntonio Nov 25 '12 at 2:48
You can always complete $A$ and $B$ to square matrices by appending zero blocks to them (and in the case of "tall" matrices, also append a zero vector to $v$). So I don't see much difference between the square and non-square cases. – user1551 Nov 25 '12 at 10:28