# eigenvalue column sum equals one linear algebra

What does the following imply about the eigenvalues of an $n\times n$ matrix $A$:

The sum of the entries in each column equals $1$.

Thank you!

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Why did you tag this with numerical-linear algebra tag ? – Belgi Jan 25 '13 at 10:03
because of the warning of "quality standards" sorry about that.. – Salih Ucan Jan 25 '13 at 10:14
If that was the reason then I removed the tag for you – Belgi Jan 25 '13 at 10:20

Hint: Prove that if the sum of every row is a constant $k$ then $k$ is an eigenvalue of $A$ with a corresponding eigenvector $(1,...,1)^{T}$.
Recall that $k$ is an eigenvalue of $A$ if and only if $k$ is an eigenvalue of $A^{T}$