The discussion focuses on constructing an orthonormal system from the functions 1, x, and 3x² - 1, emphasizing the necessity of using linear algebra techniques, specifically the Gram-Schmidt process. The inner product is likely defined in terms of an integral, which ties back to calculus concepts. Participants highlight the importance of integrating knowledge from both linear algebra and calculus to solve the problem effectively.
PREREQUISITESStudents in calculus and linear algebra courses, educators teaching mathematical concepts, and anyone interested in the application of orthonormal systems in mathematical analysis.
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!