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10 Nov 2019
Consider the vector space P2 of polynomials of degree at most 2. Define an inner product on P2 by (this is an example of an evaluation inner product). Show that the four axioms for a real inner product space (Section 6.1, Definition 1 in the text) are satisfied by this inner product. Now let p(x) = x2 - x + 1 and q(x) = x 2 - 2x - 1. Compute: The inner product The norms ||p||, ||q||. The distance d(p, q) between p and q.
Consider the vector space P2 of polynomials of degree at most 2. Define an inner product on P2 by (this is an example of an evaluation inner product). Show that the four axioms for a real inner product space (Section 6.1, Definition 1 in the text) are satisfied by this inner product. Now let p(x) = x2 - x + 1 and q(x) = x 2 - 2x - 1. Compute: The inner product The norms ||p||, ||q||. The distance d(p, q) between p and q.