Answer to Question #13068 in Linear Algebra for Jess
we consider their intersection W, then choosing base w_1,...,w_k in W, be can
compeate it to the base of U by vectors u_1,...,u_m.
Then we can choose any
vector v_0 from V, that is not linear combination of vectors from W. Then
v_0, w_1,...,w_k, u_1,...,u_m are linearly independent, and vector v_0 can
be ortogonalized to all other these vectors, thus
it will be orthogonal to U.
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