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Linear Algebra: inner product

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data
    State why (u,v) is not an inner product for u=(u1,u2) and v=(v1,v2) in R2
    (u,v)=-u2v2

    2. Relevant equations
    (u,v)=(v,u)
    c(u,v)=(cu,v)
    (v,v)=>0 and (v,v)=0 if only if v=0

    3. The attempt at a solution
    I am having trouble understanding this problem and how to start it. Please help. Thank you
     
  2. jcsd
  3. Apr 12, 2010 #2
    I would think that axiom 4 is not satisfied.
    if u=(1,2) and v=(2,2), then -u2v2=-4, which is less than 0, which violates axiom 4 that states (v,v) greater than or equal to 0. Is this right?
     
  4. Apr 12, 2010 #3

    lanedance

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    Homework Helper

    I think the axiom you refer to only guarantees positive definiteness for the inner product of a vector with itself (v,v), though it shouldn't be hard to alter you argument to work in that case

    note the inner product of 2 arbitrary vectors can be negative
     
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