What's fascinating is that the Pythagorean theorem can be extended to inner product spaces in terms of norms. product construction. Can the proof about direct sum decomposition of the inner product space be generalize to infinitely dimension space 5 Prove/Disprove an inner product on a complex linear space restricted to its real structure is also an inner product ****PROOF OF THIS PRODUCT BEING INNER PRODUCT GOES HERE**** ****SPECIFIC EXAMPLE GOES HERE**** Since every polynomial is continuous at every real number, we can use the next example of an inner product as an inner product on P n. Each of these are a continuous inner product on P n. 2.4. For example, for the vectors u = (1,0) and v = (0,1) in R2 with the Euclidean inner product, we have 2008/12/17 Elementary Linear Algebra 12 However, if we change to the weighted Euclidean inner product __= +__

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