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Math Help - Matrices and multiplication commutativity

  1. #1
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    Red face [Solved] Matrices and multiplication commutativity

    In a proof I am studying a step uses a propriety of matrices I do not know, doing some tries it seems true but I can't find a way to prove it.

    I'll use some almost-LaTeX

    v \in R^{n \times 1}
    u \in R^{1 \times n}
    the propriety is:
    (vu)^2 = (uv)(vu)

    Where, of course, (uv) is a real number.

    Probably I am just missing the obvious, but matrices multiplication isn't usually commutative. Those matrices are peculiar since made from products of vectors, but I can't see why it works.
    Can you tell me how to prove it? (or prove it is wrong of course)

    (btw, where can I find some instruction about how to use the [ math ][ /math ] mode?)

    Thanks!
    Last edited by ematb; June 25th 2008 at 12:33 AM. Reason: Solved.
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by ematb View Post
    In a proof I am studying a step uses a propriety of matrices I do not know, doing some tries it seems true but I can't find a way to prove it.

    I'll use some almost-LaTeX

    v \in R^{n \times 1}
    u \in R^{1 \times n}
    the propriety is:
    (vu)^2 = (uv)(vu)

    Where, of course, (uv) is a real number.

    Probably I am just missing the obvious, but matrices multiplication isn't usually commutative. Those matrices are peculiar since made from products of vectors, but I can't see why it works.
    Can you tell me how to prove it? (or prove it is wrong of course)
    You only need Associativity.

    By definition, (vu)^2 = (vu)(vu)

    Now by associativity:

    (vu)^2 = (vu)(vu) = v(uv)u

    Now since (uv) is a real number, v(uv) = (uv)v, thus

    (vu)^2 = (vu)(vu) = v(uv)u = (uv)vu

    Hope it helps.

    (btw, where can I find some instruction about how to use the [ math ][ /math ] mode?)Thanks!
    Just put whatever you did between these tags.

    Here is an example:

    Type [tex]v \in R^{n \times 1}[/tex] to get the following symbol: v \in R^{n \times 1}
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  3. #3
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    Thanks a lot, this explain everything.
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