16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.2.17

Inner Product Spaces

Mathematics — Linear Algebra · orthogonal-complement

Problem

Let VV be the real inner product space consisting of the space of real-valued continuous functions on the interval, −1≤t≤1-1 \leq t \leq 1, with the inner product (f∣g)=∫−11f(t)g(t) dt.(f|g) = \int_{-1}^1 f(t)g(t)\, dt. Let WW be the subspace of odd functions, i.e., functions satisfying f(−t)=−f(t)f(-t) = -f(t). Find the orthogonal complement of WW.

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