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Math Help - Matrix problem

  1. #1
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    Matrix problem

    If A=\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}, find c,d

    so that (c  I + d A)^2 = A
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  2. #2
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    Quote Originally Posted by flintstone View Post
    If A=\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}, find c,d

    so that (c  I + d A)^2 = A

    I will assume that c and d are scalar constants, while I is the indentitiy matrix. Let's start out by doing some of the small arithmetic:

     cI = \begin{pmatrix}c & 0 \\ 0 & c\end{pmatrix}

     dA = \begin{pmatrix}0 & d \\ -d & 0\end{pmatrix}


     <br />
cI + dA = \begin{pmatrix}c & d \\ -d & c\end{pmatrix}<br />



     <br />
(cI + dA)^2 = \begin{pmatrix}c & d \\ -d & c\end{pmatrix}<br />
\begin{pmatrix}c & d \\ -d & c\end{pmatrix} =<br />
\begin{pmatrix}c^2-d^2 & 2cd \\ -2cd & c^2-d^2\end{pmatrix}<br />


    Now you should be able to set your c's and d's so that the matrix looks all like original A again.

    -Andy
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