The discussion revolves around constructing an orthonormal system from the functions 1, x, and 3x² - 1. The context is within a calculus course, and participants are exploring the relationship between linear algebra concepts and calculus techniques.
The conversation is ongoing, with some participants offering insights into the necessity of linking concepts from different areas of mathematics. There is an acknowledgment of the need for clarification regarding the inner product involved in the orthonormal system construction.
Participants note that the orthogonal functions are defined with respect to a weight function of 1 over the interval [-1, 1], which may influence the approach taken in the problem.
Well an "orthonormal set" is an object out of linear algebra so you're not going to be able to avoid using techniques out of linear algebra. You'll probably have to use the Gram-Schmidt process. But that depends specifically on the inner product you're using and since you didn't specify what that is, I can't really help you much more than this. (The inner product is probably defined in terms of an integral and that's where the calculus exercise would come in.)overseastar said:I have a homework question asking to construct an orthonormal system from the three functions: 1, x, 3x^2 - 1, I know we can approach it using linear algebra method, but as this is a calculus course, I don't think that's what my prof wants us to use. Can anyone guide me through this? Thanks a bunch!