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Math Help - kernel of a set of matrices

  1. #1
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    kernel of a set of matrices

    I have to show 0= T(A)=A+A^T
    A=[a b].
    ///[c d]

    I got it to where [2a c+b]=[0 0]
    ///////////////////[b+c 2d]//[0 0]

    I know a=d=0 and b=-c. but then i can seem to figure out why the answer is
    ker T={[0 -b]
    ////////[b 0] where b is a real number}
    how do they get that?
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  2. #2
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    Re: kernel of a set of matrices

    would it make more sense to you if they used "c" instead of "b"? it's just a place-holder, any symbol could have been used.
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  3. #3
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    Re: kernel of a set of matrices

    Oh OK. I get that its just placeholders but since c=-b the wouldn't it just be [0 -b][-b 0]?
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  4. #4
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    Re: kernel of a set of matrices

    the upper-right (1,2)-entry must be the NEGATIVE of the (2,1)-entry, so:

    \begin{bmatrix}0&-b\\-b&0 \end{bmatrix}

    won't work. change one of those b's to a positive one and you have a winner.
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  5. #5
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    Re: kernel of a set of matrices

    Oh got it. Thanks I figured out why. It has to satisfy A+A^T=0.
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