Abstract
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>. |
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© 1986 Springer Science+Business Media New York
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Lang, S. (1986). Scalar Products and Orthogonality. In: Introduction to Linear Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1070-2_6
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DOI: https://doi.org/10.1007/978-1-4612-1070-2_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7002-7
Online ISBN: 978-1-4612-1070-2
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