Jacobi convergence for a three-by-three equicorrelation matrix
= Jacobi convergence for a three-by-three equicorrelation matrix
For a three-by-three matrix with diagonal entries one and every off-diagonal entry $\alpha$, the <Jacobi method> iteration matrix has eigenvalue $-2\alpha$ on the all-ones vector and eigenvalue $\alpha$ with multiplicity two on its orthogonal complement. Its <spectral radius> is $2|\alpha|$, so Jacobi iteration converges exactly when $|\alpha|<1/2$.