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Published in:
1987 | OriginalPaper | Chapter
Inner-Product Spaces, Euclidean Spaces
Author : Walter Noll
Published in: Finite-Dimensional Spaces
Publisher: Springer Netherlands
Included in: Professional Book Archive
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As in Chap.2, the term “linear space” will be used as a shorthand for “finite dimensional linear space over ℝ”. However, the definitions of an inner-product space and a Euclidean space do not really require finite-dimensionality. Many of the results, for example the Inner-Product Inequality and the Theorem on Subadditivity of Magnitude, remain valid for infinite-dimensional spaces. Other results extend to infinite-dimensional spaces after suitable modification.