Suppose some matrix $\mathbf A$ has a radical eigenvalue $\lambda$. To find a corresponding eigenvector $\mathbf v$ one can do Gaussian Elimination on the system of simultaneous linear equations represented by the matrix $\mathbf A- \lambda\mathbf I$. The presence of radicals along the diagonal makes this a cumbersome and tedious process. Is there a more efficient way to MANUALLY calculate $\mathbf v$ ?
My math (engineering) professor recommended something he calls the method of Grassmann-Steinitz in case of irrational eigenvalues. However, searching the internet turns up nothing by that name.
Any help is appreciated. Thanks in advance.