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14. If d is a metric on a vector space X‡ {0} which is obtained from a norm, and å is defined by ã(x, x) = 0, ã(x, y) = d(x, y)+1 (x‡y), show that a cannot be obtained from a norm.

14. If d is a metric on a vector space X‡ {0} which is obtained from a norm, and å is defined by ã(x, x) = 0, ã(x, y) = d(x, y)+1 (x‡y), show that a cannot be obtained from a norm.

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.CM: Cumulative Review
Problem 24CM
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14. If d is a metric on a vector space X‡ {0} which is obtained from a norm, and å is defined by ã(x, x) = 0, ã(x, y) = d(x, y)+1 (x‡y), show that a cannot be obtained from a norm.
Transcribed Image Text:14. If d is a metric on a vector space X‡ {0} which is obtained from a norm, and å is defined by ã(x, x) = 0, ã(x, y) = d(x, y)+1 (x‡y), show that a cannot be obtained from a norm.
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