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Math Help - Linear Algebra

  1. #1
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    Linear Algebra

    apply gershgorin's theorem to the problem of bounding the real and imaginary parts of the eigen values of the matrix
    A =
    (3, 0, -1, -1/4, 1/4)
    (0, 5, 1/2, 0, 1)
    (-1/4, 0, 6, 1/4, 1/2)
    (0, -1, 1/2, -3, 1/4)
    (1/6, -1/6, 1/3, 1/3, 4)
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  2. #2
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    Re: Linear Algebra

    The bounds will be for each row a_{ii} \pm \sum |a_{ij}| where i \neq j
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  3. #3
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    Re: Linear Algebra

    can u please explain further as to how to do the problem
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  4. #4
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    Re: Linear Algebra

    For the first row \displaystyle 3\pm (|0|+|-1|+|-0.25|+|0.25|) = 3\pm\frac{3}{2}

    What do you get for the second?
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  5. #5
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    Re: Linear Algebra

    for second = 5 +- 3/2
    for third = 6 +- 1
    for fourth = -3+- 7/4
    for fifth = 4 +- 1
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  6. #6
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    Re: Linear Algebra

    what are the real and imaginary eigen values of the matrix
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  7. #7
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    Re: Linear Algebra

    Looks like you have the hang of it.

    You are required to plot those intervals on the real(x)/imaginary(y) axis. In your case they all sit on x.
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