Is there a shortcut to finding out if a particular operation is an inner product? Applying the axioms takes a long time especially when in exams so is there a quick way to find out if the operation is correct according to the 5 axioms?
2026-04-19 03:49:20.1776570560
Inner product axioms
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I don't think there is any "shortcut" so to speak. There are no easier sufficient conditions for a binary operation to be an inner product. However, for exam purposes you could write proofs that the operation satisfies all axioms required very briefly, excluding justifications for trivial steps (for example, to show that integral of product is an inner product, you need not justify why the integral is a linear operation; just write it out) as they are generally easy and have only a couple of computational simplification steps. Surely your instructor would not require you to give a full proof with justifications for each step.