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11. Let (V,(, )) be a complex inner product space. For vectors v, w, set (v, w)r = 1/[(v, w)+(w, v)]. Consider V to be a real vector space. Is (V, (, )R) an inner product space? Support your answer with a proof.

11. Let (V,(, )) be a complex inner product space. For vectors v, w, set (v, w)r = 1/[(v, w)+(w, v)]. Consider V to be a real vector space. Is (V, (, )R) an inner product space? Support your answer with a proof.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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11. Let (V, (, )) be a complex inner product space. For vectors v, w, set (v, w) R = ¹/[(v, w)+(w, v)]. Consider V to be a real vector space. Is (V, (, )R) an inner product space? Support your answer with a proof.
Transcribed Image Text:11. Let (V, (, )) be a complex inner product space. For vectors v, w, set (v, w) R = ¹/[(v, w)+(w, v)]. Consider V to be a real vector space. Is (V, (, )R) an inner product space? Support your answer with a proof.
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