.Let U and W be orthogonal subspaces.
a) Prove that
If then as we get , with <,> the inner product in the v.s.
b) If is a linearly independent subset of U and is a linearly independent subset of W, prove that is a linearly independent set in V.
Suppose the definition field, then . Deduce from here and (a) above that .
I find this bit a little hard to understand, and I have to multitask, so I'll have difficulty if I have to do this on my own. Any help would be greatly appreciated.