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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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    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.2012-11-25

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Matrices A and B need not be square. But general algorithms does not work there. Please refer to papers where there is work done on non square matrices. Try searching generalized eigenvalue problem for non square matrices.