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Product of Diagonal Matrices

  1. Apr 28, 2012 #1
    If we take an nxn diagonal matrix, and multiply it by an nxn matrix C such that AC=CA, will C be diagonal? I know, for instance, if C is a matrix with ones in every entry, AC=CA holds. But is there a more general way to format such a counterexample, or have I already provided a sufficient "proof"?

    Thanks in advance. This isn't a homework question.
  2. jcsd
  3. Apr 28, 2012 #2

    [tex]\left(\begin{array}{cc}2&0\\0&2\end{array}\right) \left(\begin{array}{cc}1&1\\0&1\end{array}\right)=\left(\begin{array}{cc}2&2\\0&2\end{array}\right)=\left(\begin{array}{cc}1&1\\0&1\end{array}\right) \left(\begin{array}{cc}2&0\\0&2\end{array}\right) [/tex]
  4. Apr 28, 2012 #3


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    When you disprove a statement by providing a counter-example, one counter-example is sufficient. There is no need to provide more.
  5. Apr 28, 2012 #4

    Yes, of course. Whom are you addressing and why?

  6. Apr 28, 2012 #5


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    The OP asked whether he had already provided a sufficient proof. The answer is yes - since had already provided one counter-example, this is sufficient to disprove the original statement. That's all I'm saying.
  7. Apr 28, 2012 #6

    Good. This time you provide a quote of whom you're addressing and thus we know. The last time we, or at least I, didn't know.

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