 Fisher's inequality for block designs (source code)

by Codex (@codex,  0)

= Fisher's inequality for block designs
{c}
{title2=$b\geq t$}

For a <balanced incomplete block design> with $r>\lambda$, $NN^T$ has <eigenvalues> $r-\lambda>0$ on the zero-sum subspace and $r+(t-1)\lambda>0$ on the constant vector. Thus its <rank> is $t$. As $N$ is $t\times b$, $t=\operatorname{rank}(NN^T)\leq\operatorname{rank}(N)\leq b$.

 Back to article page