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First, we can freely choose the top rows. That's free choices.
Now we just have the middle row left (row ). In this row, the symmetry rule is . We can freely choose the first entries (the left half plus the center), and the rest are determined.
The total number of free choices is . Since and , this comes out to .
You could have answered your question if you had taken a few seconds to google "centrosymmetric matrix". In any case, lighten up. This article was just created a few hours ago, so it will take a while for the connections with other areas to be added, preferably by experts. It is not reasonable to expect that the first incarnation of an article will explain the larger significance of its subject. Centrosymmetric matrices are primarily of interest in numerical analysis, and also because they occur naturally as the transition matrices of certain types of Markov processes. The reference to Weaver's paper I added a few minutes ago might help you. Michael Kinyon01:27, 21 September 2006 (UTC)[reply]
You could have said it that way instead of heading the section with "So?". It's better to encourage than provoke. Anyway, I will assume good faith and accept your explanation. And thank you for reminding me that x should be × in the dimensions for matrices. Michael Kinyon02:51, 21 September 2006 (UTC)[reply]