E 2 2 aa(a'a L 4 E aa+ ( ∵a≠0→aa≠0,a(ma)=(aa)aa 4 4 AA=E aa+ aa=E 故A是正交矩阵T T T T T T T T T T T T T 2 T T T T T T T T T T 2 2 ( ) ( ) 2 2 [ ][ ] ( ) ( ) 4 4 [ ( ) ] ( ) ( ) 0 ( ) ( ) 4 4 ( ) ( ) = − − + = − +    =  = − + = E aa aa a a a a aa aa a a a a E aa a a a a a a a a a 0 a a a a a a a a aa A A E aa aa E a a a a A ， 故 是正交矩阵