Suppose vinV and v!=0 . Prove that (v)/(| |) |v|| | is the unique closest element on the unit sphere of V to v . More precisely, prove that if uinV and ||u||=1 , then ||v-(v)/(||v||)||<=||v-u||,

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04-06-2024
Mathematics

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Suppose vinV and v!=0 . Prove that (v)/(| |) |v|| | is the unique closest element on the unit sphere of V to v . More precisely, prove that if uinV and ||u||=1 , then ||v-(v)/(||v||)||<=||v-u||,

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Suppose vinV and v!=0 . Prove that (v)/(| |) |v|| | is the unique closest element on the unit sphere of V to v . More precisely, prove that if uinV and ||u||=1 , then ||v-(v)/(||v||)||<=||v-u||,

Sagot :

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