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Math Help - Inner Product Axioms

  1. #1
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    Inner Product Axioms

    Hello,

    I would appreciate your help on the following problem.

    A rule being used to define the mathematics of a vector space is
    <br />
<\vec{u},\vec{v}>=u_{1}v_{2}+u_{2}v_{1}<br />
    Determine and state which axiom fails.

    I tried the four axioms (symmetry, additive, homogeneity, and positive definite), but none seems to fail. Am I missing anything?

    Thank you in advance!
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  2. #2
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    Quote Originally Posted by hasanbalkan View Post
    Hello,

    I would appreciate your help on the following problem.

    A rule being used to define the mathematics of a vector space is
    <br />
<\vec{u},\vec{v}>=u_{1}v_{2}+u_{2}v_{1}<br />
    Determine and state which axiom fails.

    I tried the four axioms (symmetry, additive, homogeneity, and positive definite), but none seems to fail. Am I missing anything?

    Thank you in advance!
    it's not positive definite! for example consider u=v=(1,-1).
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  3. #3
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    Also notice that the inner product of <1, 0> with itself is <1, 0>.<1, 0>= 1(0)+ 0(1)= 0.
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