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Published in:
1986 | OriginalPaper | Chapter
Scalar Products and Orthogonality
Author : Serge Lang
Published in: Introduction to Linear Algebra
Publisher: Springer New York
Included in: Professional Book Archive
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LetVbe a vector space. Ascalar productonVis an association which to any pair of elements (v, w) ofVassociates a number, denoted by <v, w>, satisfying the following properties:SP 1.We have <v, w> = <w, v> for all y, w in V.SP 2.If u, v, w are elements of V, then <u, v + w > = <u, v> + <u, w>.SP 3.If x is a number, then <xu, v> = x<u, v> = <u, xv>.