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Consider the mapping (·, ·) : R" × R” → R defined by n (u,v) = |ui||vi|, Vu, v€ Rn. i=1 Show which defining properties of inner products are satisfied by this mapping. Provide a counterex- ample for properties not satisfied.

Consider the mapping (·, ·) : R" × R” → R defined by n (u,v) = |ui||vi|, Vu, v€ Rn. i=1 Show which defining properties of inner products are satisfied by this mapping. Provide a counterex- ample for properties not satisfied.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 94E
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Consider the mapping (·, ·) : R" × R” → R defined by n (u,v) = |ui||vi|, Vu, v€ Rn. i=1 Show which defining properties of inner products are satisfied by this mapping. Provide a counterex- ample for properties not satisfied.
Transcribed Image Text:Consider the mapping (·, ·) : R" × R” → R defined by n (u,v) = |ui||vi|, Vu, v€ Rn. i=1 Show which defining properties of inner products are satisfied by this mapping. Provide a counterex- ample for properties not satisfied.
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