If there is a Jordan block matrix with $A(i,i) = a$ for all $i=1$ to $n$, $A(i,i+1)=b$ for all $i=1$ to $n-1$ and $A(j,k)=0$ otherwise. What will be eigenvalue and eigenvector of $J$?
To calculate eigenvalues I split the matrix in a diagonal matrix $= diag(a)$ and another matrix $B$ with $A(i,i+1)=b$. As $B$ is singular matrix, one of the eigenvalues will be zero. So for Jordan block matrix eigenvalue become $=a+0 =a$. How to find rest of the eigenvalues and eigenvectors?