I was sitting in McDonald's waiting for my food when I noticed a 4x5 matrix of plates arranged above the counter. The diagonals of this matrix alternated in plates embossed with either red or yellow Ms. It got me thinking, given a random matrix, in R, or Z, or Z_p, and given the m+n-1 diagonal sums, about a few questions concerning this.
Can we determine m and n? What kinds of confidences or probabilities can we determine m and n with? Are these different for the different cases?
I didn't see anything obvious at first, so I thought I would ask here.
Let us not assume anything special about the distribution of elements of the matrix. So I guess that is called a 'random matrix'.
