A,B是m阶对称阵,则 AB对称台AB=BA A=A,B=B,:(AB)=BTAT =BA =AB 故AB是对称阵 “→”.AB是对称阵,AB=(AB)=BA1=BA [A,B是n阶对称阵，则 AB 对称 ⇔ AB = BA 证 A A,B B, T T Q = = T T T ∴(AB) = B A = BA = AB “⇐” A A,B B, T T Q = = T T T ∴(AB) = B A = BA = AB 故AB是对称阵。 “⇒” T Q AB是对称阵，∴ AB = (AB) T T ＝B A = BA