We have . Taking norms we obtain . But . As < , necessarily which implies for all .
there is a group of vectors in ,there is orthonormal basis of .
the first part i have proved that for in R
the second part is my question
prove that if is a set for which then is independant?
how i tried to solve it:
a set is independant if for the only way it to be zero is if k1=..=kn=0
i opened it and got
so on both side we have equal vectors so is their norm
what next how to prove that