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Thread: Matrix multiplication and the dot product (HW)

  1. #1 Matrix multiplication and the dot product (HW) 
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    Suppose that A is an n x n matrix such that A(Transpose)A=I. Let x be any vector in R^n. Show that llAxll=llxll; that is, multiplication of x by A produces a vector Ax having the same length as x.

    Relevant equations

    Sqrt(x(transpose)x)=llxll

    The attempt at a solution

    So I started setting up the equation wth an n x n matrix...

    l a b l =A
    l c d l

    l a c l= A (transpose)
    l b d l

    A(transpose)A= I=
    l a^(2) +c^(2) ab+cd l
    l ba+dc b^(2)+d^(2)l

    then I let the vector x=

    l x1 l
    l x2 l


    then from there I was going to use the distance formula on Ax

    but I wasn't sure if doing the dot product of Ax is the same thing as matrix multiplication of Ax, and my second problem is that I am not sure how to take the square root of a 2x2 matrix if they are the same thing.

    If someone can answer those to questions for me I think I can finish the problem.

    Thank you.


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  3. #2  
    Forum Ph.D. Leszek Luchowski's Avatar
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    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
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