Question: are eigenvectors of a matrix a corresponding to the eigenvalues?
Answer: The scalar λ is called an eigenvalue of T (the matrix A) and the nonzero vector v is called an eigenvector of T (of the matrix A) corresponding to the eigenvalue λ. ... Note that the set of eigenvectors of A corresponding to the zero eigenvalue is the set Nul A − {0}; and A is invertible if and only if Nul A = {0}.