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Homework Help: Is this a diagonal matrix

  1. Dec 26, 2003 #1
    diagonal matrix is a matrix with each element is0 excep for elements on the major diagonal.

    so, does it mean that

    ( 2 0 0
    0 0 0
    0 0 3 )

    is not a diagonal matrix??
     
  2. jcsd
  3. Dec 26, 2003 #2

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    A (square) matrix is diagonal iff the nondiagonal entries are zero.

    The diagonal entries are permitted to be zero as well, so this matrix is diagonal, with diagonal entires 2, 0, and 3:

    [tex]
    \left(
    \begin{array}{ccc}
    2&0&0 \\
    0&0&0 \\
    0&0&3
    \end{array}
    \right)
    [/tex]


    (Yes, I am using this post as an excuse to get more practice writing in LaTeX. :smile:)
     
  4. Dec 26, 2003 #3

    HallsofIvy

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    Science Advisor

    To extend Hurkyl's answer, the conditional in the Hurkyl's definition is:
    " the nondiagonal entries are zero". That says nothing about numbers on the diagonal which may be zero or non-zero,

    Your statement:
    "each element is 0 except for elements on the major diagonal."
    is a slightly ambiguous way of saying the same thing.

    The ambiguity could be removed by saying:
    "each element is 0 except possibly for elements on the major diagonal."
     
  5. Dec 26, 2003 #4
    all righttt.. thank you.
     
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