 λ_{i} are eigenvalues of A and A ≠ 0
 One of the eigenvalues of A is zero
 λ_{i} are eigenvalues of A and λ_{i} ≠ 0 for all i
 λ_{i} are eigenvalues of orthogonal matrix A
 A, B, P are nsquare matrices P ≠ 0 and B=P^{–}^{1}AP
 D = [d_{ij}]is an nsquare matrix with d_{i}_{j} = 0 for i ≠ j
 Characteristic polynomials of A and A^{2}are same
 Characteristic equation of A is λ^{m} = 0
 A is orthogonal

 A is singular
 1 / λ_{i} are also eigenvalues of A
 A and B are similar
 A  / λ_{i } are eigenvalues of Adj A
 A is nonsingular
 Characteristic polynomials of A and B are same
 d_{ii} are eigenvalues of D
 Characteristic equation of A is a reciprocal equation
 A is idempotent
 A is nilpotent with index m
