If c is an eigenvalue of $A$, is it an eigenvalue of $A^{\mathbf{T}}$? I am given a square matrix $A$, and I need to prove that if c is its eigenvalue, then it is also an eigenvalue of its transpose. How should I approach this? Clearly $Av$=$cv$, but I am not sure how to bring transpose into the equation.

Another way to look at it is to see that it's equivalent to the following statement: $A$ is regular iff $A^T$ is regular. That follows from the fact that the row rank is equal to the column rank. But I'm not sure how easy it is to show that directly. Anyone?
