Unformatted text preview: Q ( λv ) = λ 2 Q ( v ) for each λ ∈ R and v ∈ V . (b) Show how the polarization identity provides a means of deﬁning a symmetric bilinear map given a quadratic function on a vector space. 5. Let [ a,b ] be an interval and let L 2 ([ a,b ]) be the set of functions f : [ a,b ] → R whose square is integrable over [ a,b ]. We refer to such functions as squareintegrable . Show that the map ( f,g ) 7→ R b a f ( t ) g ( t ) dt is an inner product. This map is referred to as the L 2 ([ a,b ])inner product; it is convenient to denote it by ± f,g ² L 2 ([ a,b ]) . 6. For V a ﬁnitedimensional Rvector space, show that the following pairs of vector spaces are naturally isomorphic by providing explicit isomorphisms: (a) T 1 ( V ) and V ; (b) T 1 ( V ) and V * ; (c) T 1 1 ( V ) and L ( V ; V ); (d) T 2 ( V ) and L ( V ; V * ); (e) T 2 ( V ) and L ( V * ; V ). 1...
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This note was uploaded on 03/06/2010 for the course MEDICAL EN AEM570 taught by Professor Kristia.morgansen during the Spring '10 term at University of Western States.
 Spring '10
 KristiA.Morgansen

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