Linear Algebra 42 Orthogonal Complements and Decompositions

We will show how to use the Gram Schmidt Algorithm to construct a basis for the orthogonal complement of a subspace W of an inner product space V. We will also show how to decompose an arbitrary vector v from V into a sum v = w1 + w2, where w1 is from W, and w2 is from the orthogonal complement of W.