There are two possible definitions of the phrase ''period matrix'' discussed in the following post: http://www.martinorr.name/blog/2015/10/06/periods-of-abelian-varieties/
Is there a concrete example of how to convert from the $g \times 2g$ form to the $2g \times 2g$ one (the ``extended period matrix'' in the post)? In particular, the post says that the $g \times 2g$ matrix is the transpose of the left half of the $2g \times 2g$ matrix in the section "Relationship between the two-period matrices''. What does the other half look like? Since the resulting matrix should be in the Siegel upper half-space $\mathfrak{h}_{2g}$, it looks like the upper right block should be the same as the lower left blow since the matrix needs to be symmetric. But I'm not sure how to make this compatible with the dualization or what the last block should be in general.
Note: I realize this question is very similar to another one that I posted earlier (Period matrix conventions), but that one hasn't received any responses for a long time.