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Non-Square Skew (Symmetric/Repeating) Matrix?

  1. Oct 23, 2012 #1
    Hi,

    I am preparing to publish an academic article on computational efficiency and image processing. In my work, I have come across what I can best describe as a non-square skew (symmetric or repeating) matrix (I know it can't be symmetric since it's non-square).

    Here are some examples of what it may look like:

    (9 x 2)

    \begin{array}{cc}
    0 & -6 \\
    0 & -6 \\
    0 & -6 \\
    3 & -3 \\
    3 & -3 \\
    3 & -3 \\
    6 & 0 \\
    6 & 0 \\
    6 & 0 \end{array}


    (16 x 3)

    \begin{array}{ccc}
    0 & -12 & -24 \\
    0 & -12 & -24 \\
    0 & -12 & -24 \\
    0 & -12 & -24 \\
    8 & -4 & -16 \\
    8 & -4 & -16 \\
    8 & -4 & -16 \\
    8 & -4 & -16 \\
    16 & 4 & -8 \\
    16 & 4 & -8 \\
    16 & 4 & -8 \\
    16 & 4 & -8 \\
    24 & 12 & 0 \\
    24 & 12 & 0 \\
    24 & 12 & 0 \\
    24 & 12 & 0 \end{array}

    (4 x 6)

    \begin{array}{cccccc}
    0 & -2 & -4 & -6 & -8 & -10 \\
    0 & -2 & -4 & -6 & -8 & -10 \\
    10 & 8 & 6 & 4 & 2 & 0 \\
    10 & 8 & 6 & 4 & 2 & 0 \end{array}


    Is there a specific name for this type of matrix? If so, I could not find one.

    Also, what are some properties of this matrix that I may be overlooking?

    1) It seems that the rank will always be 2.
    2) (If the matrix is A): AA' and A'A is always symmetric.


    Thank you for your time.
     
  2. jcsd
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