(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Are there references of the following structured matrix?

A =

1 0 1 0 0

1 0 0 1 0

1 0 0 0 1

0 1 1 0 0

0 1 0 1 0

0 1 0 0 1

;

Say we have group A=1,2; group B=1,2, 3; the rows of above matrix shows all possible selections: one element from each group. Hence A corresponding to the list:

11

12

13

21

22

23

;

B =

1 0 1 0 0 1 0 0

1 0 1 0 0 0 1 0

1 0 1 0 0 0 0 1

1 0 0 1 0 1 0 0

1 0 0 1 0 0 1 0

1 0 0 1 0 0 0 1

1 0 0 0 1 1 0 0

1 0 0 0 1 0 1 0

1 0 0 0 1 0 0 1

0 1 1 0 0 1 0 0

0 1 1 0 0 0 1 0

0 1 1 0 0 0 0 1

0 1 0 1 0 1 0 0

0 1 0 1 0 0 1 0

0 1 0 1 0 0 0 1

0 1 0 0 1 1 0 0

0 1 0 0 1 0 1 0

0 1 0 0 1 0 0 1

;

group A=1,2; B=1,2,3; C=1,2,3; and the above matrix indicating the list:

111

112

113

121

122

123

131

132

133

211

212

213

221

222

223

231

232

233

;

2. Relevant equations

Say the number of elements in a group and number of groups are arbitrary, then the linear system Ax=b, b not zero sometimes have solution; most time it is over determined, and a least square solution is x = (A'A)^-1A'b if (A'A) is invertible, when it is invertible?

3. The attempt at a solution

(A'A) is invertible and its inverse is visually appealing:

0.25000 0.50000 -0.25000 0.00000

-0.25000 0.00000 0.25000 0.50000

0.50000 -0.25000 0.50000 -0.25000

0.00000 0.25000 0.00000 0.25000

(B'B) is singular from Octave.

It seems that is a pattern, but it is pretty hard to derive it. Is this matrix a well known matrix?

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# What Matrix is this?

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