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!
[Math] eigenvalue column sum equals one linear algebra
linear algebra
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!
Best Answer
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 $A^{T}$