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Thread: A little linear algebra help

  1. #1
    Join Date
    Mar 2004
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    A little linear algebra help

    I dont understand the concept of why an arithmetic rule like (a+b)^2 = a^2 + 2ab + b^2 and (a+b)(a-b) = a^2 - b^2 doesn't work when a and b are replaced by square matrices. I can prove it by actually doing it, but what is the actual explanation for this? Is it only because matrix multiplication is not commutative or are there other reasons for why these arithmetic rules don't work for matrices?

  2. #2
    Join Date
    Aug 2004
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    2,790
    Yes. For instance, in one of the steps of the algebra, you have ab+ba. In the matrices, this will only be equal to 2ab if ba equals ab--which is the commutative property.

  3. #3
    Join Date
    Mar 2004
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    1,163
    Oh alright. Thanks! I didn't really understand what "it's not commutative" meant in the first place. Thanks a lot.

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