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Math Help - Linear Algebra Help - Question 1 !

  1. #1
    Junior Member
    Joined
    Sep 2008
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    Linear Algebra Help - Question 1 !

    Please help me in these problems

    Determine which of the four inner product axioms do not hold. give a specific example in the case.
    u v
    [u1] [v1]
    [u2] [v2]

    Let u and v be in R^2.
    define <u, v> = u1v1 - u2v2

    axioms:
    1) <u, v> = <v,u>
    2) <u, v+w> = <u, v> + <u, w>
    3) <cu, v> = c<u, v>
    4) <u, u> greater than or equal to 0 if and only if u = 0
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  2. #2
    Super Member Gamma's Avatar
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    Dec 2008
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    Iowa City, IA
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    properties 1, 2 and 3 seem good, but 4 fails.

    consider u=(1,2)^T then <u,u> = (1*1)-(2*2)=-3 \not \geq 0
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