6.6-06 Inner products of functions

Inner products of functions

Integration turns continuous functions into geometric objects with length and perpendicularity. The questions calculate products and distances, test orthogonality on specified intervals and explain why integral geometry differs from pointwise overlap.

What you will practise

• Evaluate polynomial function products.
• Compute integral norms and distances.
• Use parity and centered functions.
• Distinguish continuous-function positivity from sampled degeneracy.

Begin with recognition and interpretation, then work through calculations, error diagnosis and more demanding reasoning. Single-select and multi-select questions ask you to evaluate the stated assumptions as well as the result. Worked explanations connect the answer to a method or a counterexample, so you can check why tempting alternatives fail.

Before you start

Review the integration bridge and real inner-product axioms. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports orthogonal polynomials and approximation of functions within Module 6 of the Complete Linear Algebra Course.