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...Preview inner product spaces examples satya mandal ku summer goals concept of length distance and angle in r or rn is extended to abstract vector v such a space will be called an comes with n that like dot the euclidean only one example denition suppose on function h i associates each ordered pair u vectors real number hu vi for all w scalar c we have hv ui wi chu hcu theorem properties let two then cvi proof would use commutativity hw hcv chv proofs are complete...