Orthogonality and Least Squares Part 1

The inner product, defined on some vector space V, is a function that maps two vectors to a scalar. The inner product between vector x and y is denoted {x,y}. The inner product has 4 properties that we discuss. For the special case where the vector space is Rn, the inner product is the dot product. For this special case, the dot product between vectors x and y is simply xy^T (i.e. the product of x with the transpose of y). We work an example of computing the dot product between two vectors.