Web Reference: This page explains the orthogonal decomposition of vectors concerning subspaces in \ (\mathbb {R}^n\), detailing how to compute orthogonal projections using matrix representations. This observation provides a convenient way of calculating alternative coordinates with respect to a given basis B, as long as all vectors in this basis are orthogonal. The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as or a∥b.
YouTube Excerpt: This calculus 3 video tutorial explains how to find the
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