Bipartite block-constant positive semidefinite matrix
= Bipartite block-constant positive semidefinite matrix
For positive block sizes, the real <matrix> $\begin{pmatrix}aJ&bJ\\bJ&aJ\end{pmatrix}$ is a <positive semidefinite matrix> exactly when $a\geq|b|$. For test-vector block sums $s,t$, its <quadratic form> is $(a+b)(s+t)^2/2+(a-b)(s-t)^2/2$. This proves sufficiency; testing $s=\pm t$ proves necessity. Zero sums in both blocks describe part of its <kernel>.