$ll'\rmn{cov}(\tilde{C}_l^E,\tilde{C}_{l'}^B)$ respectively. The prefactors have been chosen to make the elements near the diagonal more nearly uniform. Given that the weight function is symmetric under parity, ${}_+ I_{(lm)(lm)'} = (-1)^{l+l'} {}_+ I_{(lm)(lm)'}$ and ${}_- I_{(lm)(lm)'} = -(-1)^{l+l'} {}_- I_{(lm)(lm)'}$, so that $\rmn{cov}(\tilde{C}_l^E,\tilde{C}_{l'}^E)$ and $\rmn{cov}(\tilde{C}_l^B,
\tilde{C}_{l'}^B)$ vanish if $l+l'$ is odd, while $\rmn{cov}(\tilde{C}_l^E,\tilde{C}_{l'}^B)$ vanishes if $l+l'$ is even (and hence on the diagonal). In each of the three covariance matrices, the intense feature for $l$ and $l' \la 50$ (which saturates the colour scale) arises predominantly from the additional power in $C_l^E$ on large scales due to reionization. (It vanishes if we substitute for power spectra with no reionization.)

In the case of $\rmn{cov}(\tilde{C}_l^E,\tilde{C}_{l'}^E)$, the first term inside the summation over $L$ and $M$ in equation (\[eq:5-37\]) is always dominant. The covariance is thus very similar to that for the temperature anisotropies with the same weight function. The matrix is diagonally dominant, except on large scales, with width inversely related to the angular dimension of the retained region. On large scales the covariance matrix is dominated by the additional polarized power generated by reionization. Note that this power propagates to somewhat smaller scales in the pseudo-$C_l$ covariance due to residual Fourier 