16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.2.15
Inner Product Spaces
Mathematics — Linear Algebra · inner-products-direct-sum
Problem
Suppose V=W1⊕W2 and that f1 and f2 are inner products on W1 and W2, respectively. Show that there is a unique inner product f on V such that
(a) W2=W1⊥;
(b) f(α,β)=fk(α,β), when α, β are in Wk, k=1,2.