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I want to make a set of matrices that satisfies all the following:

1) $A^2 = B^2$, $C^2 =D^2$..... where $A,B,C,D...$ are matrices

2) $AB = 0$, $CD = 0$.....

3) All matrices in the set commute.

4) $AC \neq 0$, $AD \neq 0$, $BC \neq 0$, $BD \neq 0$.... so other than $AB$, $CD$ ... multiplication is always nonzero.

Also, is there any mathematical object that satisfies all of these?

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    Other than Kronecker prodcut way, are there other better ways to do this?2012-10-27
  • 2
    Define "better".2012-10-27
  • 0
    By better, I mean that the size of matrices being shorter.2012-10-27

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