In the given matrix, only one eigen value is real. What is that eigen value ?
\begin{bmatrix} 1& 5& 4& 3& 2\\ 2& 1& 5& 4& 3\\ 3& 2& 1& 5& 4\\ 4& 3& 2& 1& 5\\ 5& 4& 3& 2& 1 \end{bmatrix}
Is there any small approach ?
Find the real eigen value of the following matrix?
1
$\begingroup$
matrices
eigenvalues-eigenvectors
-
1@Moo, it just completely amazes me how some people can just pull up some obscure result like that so quickly. – 2017-02-06
-
1Observe that the totals of the rows/columns are all equal. Act then by the matrix at the vector $x=(1,1,1,1,1)^T.$ You'll see that $Ax=15x,$ and so 15 is a real eigenvalue. – 2017-02-06