8. There are several norms of practical importance on the vector space of ordered n- tuples of numbers, notably those defined by ||r||1 = |£1|+ |$2l +...+ I§n| Page 12 |,= (16." + |62l° +... + 16.P)" ||. = max{|f1], ..., E1}. (1

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
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Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 43E: Prove that in a given vector space V, the zero vector is unique.
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N1 to N4 are 4 axioms of norm.

8. There are several norms of practical importance on the vector space of ordered n-
tuples of numbers, notably those defined by
||r||1 = |&1| + |£2| +...+ Ign|
Page 12
1/p
||, = (16." + |&2P° +...+ 1S.P")" (1 <p< +x)
||x|| = max{|$1|,...,\&n]}.
In each case, verify that (N1) to (N4) are satisfied.
Transcribed Image Text:8. There are several norms of practical importance on the vector space of ordered n- tuples of numbers, notably those defined by ||r||1 = |&1| + |£2| +...+ Ign| Page 12 1/p ||, = (16." + |&2P° +...+ 1S.P")" (1 <p< +x) ||x|| = max{|$1|,...,\&n]}. In each case, verify that (N1) to (N4) are satisfied.
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