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Math Help - matrix algebra

  1. #1
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    matrix algebra

    for the square matrix A can
    (I + A)^-1 be expanded or simplified. is it true (I + A)^-1 = A^-1 - I
    where I is the identity matrix
    thanks to anyone who can help
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by smiler View Post
    for the square matrix A can
    (I + A)^-1 be expanded or simplified. is it true (I + A)^-1 = A^-1 - I
    where I is the identity matrix
    thanks to anyone who can help
    No, it is not true. (It's not even true for scalars.)
    Consider:
    A = \left ( \begin{matrix} 1 & 9 \\ -4 &2 \end{matrix} \right )
    (I just randomly selected numbers here. It is not a "special" case.)

    You'll see that it doesn't work out.

    -Dan
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