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About Singular and Symmetric Matrix

  1. Sep 28, 2006 #1
    I would like to know the statement is always true or sometimes false, and what is the reason:
    A is a square matrix
    P/S: I denote transpose A as A^T
    1)If AA^T is singular, then so is A;
    2)If A^2 is symmetric, then so is A.
     
  2. jcsd
  3. Sep 28, 2006 #2

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    Is this homework? What have you tried?
     
  4. Sep 28, 2006 #3
    This is not homework, I just want to practise more.
    About the question, I have no hint whether the statement is correct or false.
    Can you give me some hint so i can start solving this problem?
     
  5. Sep 28, 2006 #4

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    Ok, if AB is singular, can you say anything about A or B? Also, when checking if a matrix is symmetric, the natural thing to do is look at its transpose.

    EDIT: Sorry, I read your second question backwards (ie, to show A^2 is symmetric if A is). As a hint for your actual question, note that the zero matrix is symmetric.
     
    Last edited: Sep 28, 2006
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