In linear algebra, we are occasionally interested in resolving vectors into their “projections.” In contrast with components, however, which are determined with respect to the x- and y-axis, projections are determined with respect to an adjacent vector, one that shares the same initial point. This blog discusses the derivation of formulas that help us in finding these projections. Suppose we have two nonzero vectors u and v in 2-space. The vector u can be written as a sum of vectors, say, and : (i) where is constructed to be parallel to the adjacent vector v and is made to be … Continue reading Orthogonal projections in linear algebra