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I am working with the square-roots of square symmetric matrices. The answers are to be binary symmetric matrices.

If we take the matrix $$M = \begin{pmatrix}1&1&1&0&0&0&0\\1&0&0&1&1&0&0\\1&0&0&0&0&1&1\\0&1&0&0&1&0&1\\0&1&0&1&0&1&0\\0&0&1&0&1&1&0\\0&0&1&1&0&0&1 \end{pmatrix},$$ then $M^2$ will yield a $7 \times 7$ matrix with $3$ down the main diagonal and $1$ elsewhere.Once we have the matrix $M^2$ then we want to take the square root of it in order to get M.Now this is the simplest of all examples that I can give. M is the incidence matrix of a symmetric balanced incomplete block design. This design has 7 varieties, 7 blocks,each variety occurs in 3 blocks,each block contains 3 varieties, each pair of varieties occurs in exactly one block. If you are familiar with block designs then the parameters are (v,b,r,k,l)=(7,7,3,3,1) known as the fano plane.

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    Please don't use caps lock.2012-06-24
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    *Please* don’t use all-caps: it comes across as SHOUTING, and it’s hard to read besides.2012-06-24
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    Beside CapsLock, what is your question, exactly?...2012-06-24

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