2
$\begingroup$

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!

  • 0
    Well, *also* regular eigenvectors are defined for square matrices, otherwise things may hardly make sense (exercise: try with a $\,2\times 3\,$ matrix...)2012-11-25
  • 0
    Regular ones do, but the definition for generalized ones seems not.2012-11-25
  • 0
    Well it seems yes, at least according to Wiki...2012-11-25
  • 1
    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

1 Answers 1