Orthogonal Complements and Orthogonal Projections onto Subspaces

We discuss the orthogonal complement of a subspace of an inner product space. This is a subspace in which every element is orthogonal to the original subspace. With this notion, we are able to construct more general projections onto subspaces. We prove that a finite dimensional space can be decomposed into the direct sum of a subspace and its orthogonal complement.
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