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

??