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Titlebook: Algebra I; Textbook for Student Alexey L. Gorodentsev Textbook 2016 Springer International Publishing AG 2016 Fields.Rings.Modules.Groups.L

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Duality, .. We have seen in Sect. . on p. 136 that every linear map is uniquely determined by its values on an arbitrarily chosen basis. In particular, every covector . ∈ .. is uniquely determined by numbers . as . runs trough some basis of .. The next lemma is a particular case of Proposition . on p. 137.
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Euclidean Spaces,= (., .) for all ., . ∈ ., (., .) > 0 for all . ≠ 0, and . for all . and all .., .., .., .. ∈ .. The first condition is called ., the second, ., and the third, .. A real vector space . equipped with an inner product is called a . vector space. An inner product on a Euclidean space is also called a .
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