In this paper, we show that if λ is an eigenvalue of a square matrix  then by using the largest non-singular sub-matrix of the matrix  we may obtain all the linearly independent right and left eigenvectors of  corresponding to the eigenvalue λ. We shall also explain how to find the limiting matrix of  if there is any.

eigenvalues, right and left eigenvectors, eigenmatrix, Jordan canonical form, algebraic multiplicity, geometric multiplicity, semi-simple, non-singular matrix, the spectrum, limiting matrix.