Scalar Products and Orthogonality
Part of the Undergraduate Texts in Mathematics book series (UTM)
Let V be a vector space over a field K. A scalar product on V is an association which to any pair of elements v, w of V associates a scalar, denoted by <v, w>, or also v·w, satisfying the following properties:
- SP 1.
We have <v, w> = <w, v> for all v, w ∈ V.
- SP 2.If, u, v, w are elements of V, then.$$<u,v+ w>=<u,v>+<u,w>$$
- SP 3.If x ∈ K, thenand$$<xu,v>= x<u,v>$$$$u,xv>=x<u,v>$$
KeywordsVector Space Scalar Product Orthonormal Basis Dual Space Orthogonal Basis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Science+Business Media New York 1987