1)A)T is a normal in V inner product space
there is M_{1}(t),M_{2}(t) different polinomial u,v\in V
prove that if M_{1}(T)u=0 and M_{2}(T)v=0 then u orthogonal to v?
how i tried:
i have defined Q_{1} and Q_{2}and proved that v is eigen vector of M_{2}(t)Q_{2}(t) of eigenvalue 0.
and u is eigen vector of M_{2}(t)Q_{2}(t) of eigenvalue 1.
so if M_{2}(t)Q_{2}(t) is normal then u is orthogonal to v.
but how to prove that M_{2}(t)Q_{2}(t) is normal?
i cant show here that TT*=T*T

MQ(MQ)*=MQQ*M*
(MQ)*MQ=Q*M*MQ
those two are not the same
??