Though it's not (quite) obvious that element [n, n] is not over-determined ... WFL On 4/29/13, Henry Baker <hbaker1@pipeline.com> wrote:
Woops! At least one of these equations is redundant, so perhaps the dimension is n^2-2n-1 = (n-1)^2.
(This part is obvious: take a random (n-1)x(n-1) matrix & pad it with one additional row & column, which consists of -row sums and -column sums.)
At 05:21 PM 4/28/2013, Henry Baker wrote:
Is there a name for matrices whose rows & columns both sum to zero ?
What about _square_ matrices of this type ?
Clearly, there are n^2 unknowns and 2n equations, so the nxn matrices have dimension n^2-2n = n(n-2).
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