Pseudo-orthogonal matrix?

orthogonal

Hey all, I have been playing around with a special type of matrix and am wondering if anyone knows of some literature about it. I have been calling it a pseudo-orthogonal matrix but would like to learn if it has a real name or if we can come up with a better name. The characteristics of the matrix are as follows:
1) The matrix is composed of only ones and zeros
2) Each row and each column have the same number of ones in it. (If there are 3 ones in each row/column then I call a 3rd order matrix)
3) Between any two rows, there is one and only one common column with a one.

Here is an example of what I call a 3rd order pseudo-orthogonal matrix. Let's call him 'M'
1 1 1 0 0 0 0
1 0 0 1 1 0 0
1 0 0 0 0 1 1
0 1 0 1 0 1 0
0 1 0 0 1 0 1
0 0 1 1 0 0 1
0 0 1 0 1 1 0

I call it a pseudo inverse because inv(M) = M/2-1/6 , i.e. with adding and multiplying by constants I can arrive at the inverse of M.

Has anyone played with something like this before? I am hoping to gleen information to help me generate higher order matrices of this type.

chiro

Hey orthogonal and welcome to the forums.

I've never played with this kind of thing (I haven't had to): do you have a reason for doing this: (pure curiosity or do you have an application in mind)?

I don't know whether this would help but error correcting code matrices (in binary XOR) might share common properties with this (it's just a hunch and its probably wrong anyway, but you never know!).

orthogonal

I am working on the applications but I found the matrix by analyzing the matching card game Spot it! It is a card game which has 8 symbols per card with one and only one matching symbol between any two cards. If you follow the link above you can play a demo.

chiro

How about considering the eigenvalues to create a higher dimensional matrix (as well as the eigenvectors)?

http://en.wikipedia.org/wiki/Matrix_diagonalization

http://en.wikipedia.org/wiki/Eigenva...her_properties

orthogonal

I have some findings to report:

I have written a program which can generate up to order 6 successfully, but when my code attempts to do order 7 it chokes (24 hours + with no solution returned!).

After googling around some more I found a poster presentation which describes the problem using mutually orthogonal Latin squares. It looks like I have some reading to do to catch up on all this higher order geometry stuff.