12.1 Orthogonal Functions


In certain areas of advanced mathematics, a function is considered to be a generalization of a vector. In this section we shall see how the two vector concepts of inner, or dot, product and orthogonality of vectors can be extended to functions. The remainder of the chapter is a practical application of this discussion.

Inner Product

Recall, if u = u1i + u2 j + u3k and v = v1i + v2 j + v3k are two vectors in R3 or 3-space, then the inner product or dot product of u and v is a real number, called a scalar, defined as the sum of the products of their corresponding components:

In Chapter 7, the inner ...

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