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Math Help - Show that the product of two upper triangular matrices is upper triangular matrix

  1. #1
    Member Jskid's Avatar
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    Show that the product of two upper triangular matrices is upper triangular matrix

    Show that the product of two upper triangular matrices is upper triangular matrix.

    I know this is true because in the lower part each term will be multiplied by 0 (so in the lower part each element will be 0(a)+0(b)...+0(z))

    My question is how do you actually write this?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint :

    If A=(a_{ij}) and B=(b_{ij}) are n\times n matrices, and AB=(c_{ij}) use:

    c_{ij}=\displaystyle\sum_{k=1}^n{a_{ik}}b_{kj}


    Fernando Revilla
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Jskid View Post
    Show that the product of two upper triangular matrices is upper triangular matrix.

    I know this is true because in the lower part each term will be multiplied by 0 (so in the lower part each element will be 0(a)+0(b)...+0(z))

    My question is how do you actually write this?
    And the characterization of "the lower half is zero" in terms of these a_{i,j}s' Dr. Revilla speaks of.
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