I am wondering about the relation between the eigenvalues of a matrix $A$ and it rows or columns. I mean can one say that $\lambda_1$ is related to $r_1$ (first row of $A$) or $c_1$ (first column of $A$)? I know you may ask then what is $\lambda_1$? But the question is, what is the relation between a specific eigenvalue of a matrix and a column or a row of the matrix?
If there is a relation between rows (or columns) and eigenvalues. Say that: $\lambda_1$ corresponds to $r_1$. If i take the transpose of A, since eigenvalues still are same, can I still say $\lambda_1$ corresponds to $r_1'$ (first row of $A'$).
This might be a little strange question, but i appreciate for any ideas.