Unformatted text preview: to the notion of an abelian group. A vector space over K is also called a K –vector space. A vector space over R is also called a real vector space and a vector space over C a complex vector space. Example 3.3.2. (a) K n is a vector space over K , and any vector subspace of K n is a vector space over K . (b) The set of K –valued functions on a set X is a vector space over K , with pointwise addition of functions and the usual multiplication of functions by scalars. (c) The set of continuous real–valued functions on Œ0;1Ł (or, in fact, on any other metric or topological space) is a vector space over R with pointwise addition of functions and the usual multiplication of functions by scalars. (d) The set of polynomials KŒxŁ is a vector space over K , as is the set of polynomials of degree ² n , for any natural number n ....
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 Fall '08
 EVERAGE
 Algebra, Group Theory, Matrices, Vector Space, 1g, 2 K, Z4

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