Is there any analytic method to find out the maximum eigenvalue given any square matrix? Or can I find out any information about the maximum eigenvalue given a square matrix?
If not, what if the matrix is specified to be a Laplacian matrix corresponding to a graph?
EDIT: I know there is a standard way to calculate the eigenvalues of a square matrix, i.e. the roots of $|\lambda I - A |= 0$. But what if this matrix is of a very large dimension? Is there a more explicit or easier way to find out the maximum eigenvalue in particular?