We consider a linear transformation defined by an \(n\times n\) matrix A. If there is a nonzero vector \(\textbf{v}\) such that \(A\textbf{v}=\lambda \textbf{v}\) for some scalar \(\lambda,\) then the scalar \(\lambda \) is called an eigenvalue of A,  and the vector \(\textbf{v}\) is called an eigenvector corresponding to \(\lambda.\)