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I have a question:

assume in matrix M(n*n), each element M(i,j) of matrix is computed as M(i&)*M(&j) / M(&&) where M(i&) is the summation of ith row, and M(&j) is the summation of jth column and M(&&) is the summation of all M(ij) for i=1..n and j=1..n. Now I want to know what is the rank of a matrix? Why?

Also what is the maximum number of missing values in matrix, such that we can compute them exactly from other values? For e.g if we have all values in first column and first row we can calculate all M(i&) and M(&j) and M(&&). Hence we can calculate all of the other values? but this the case when we have a whole row and column. I want to know in general what is the maximum number of all missing values? why?

Thanks in advance.

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# Rank of a matrix and max number of missing values

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