Non-Square Skew (Symmetric/Repeating) Matrix?

[GreenLRan]

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.

 

[fresh_42]

Except that they are somehow funny, there is no name that I knew of. Your observations look right.