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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.