What I do find interesting though is that the constructed matrices with the properties such that every row is negative and every column is positive have certain properties that suggest some columns must have more values of '1' per say then other columns. Can such a matrix exist that every column...
This is the sort of counterexample I was looking for, unfortunately I don't seem to understand the matrix you describe here. Can you addd a bit more detail for me to follow? Thanks.
Okay I am still trying to make sure I understand which infinite sum you are objecting too so I will break up my questions into parts. Let's forget the sum of the entire matrix for a second:
First question: Would it not be a contradiction to have a matrix in which every row sum is a positive...
Ok but I am not attempting to show convergence. The rows sums are always less than -1, So the sum of the matrix is equivalent to an infinite sum of the sequence a_n=-1+eps, eps>0which diverges negative infinity.
The column sums, under the assumption of infinitely many 1's, is the infinite...
Thanks for your response, I have looked into what you have said and see how the series you created can converge to both negative and positive infinity...
However, I don't see how you could possibly rearranged the constructed matrix in my result and do the same thing. For example:
Consider...
I know that there is likely an error somewhere in my solutions to these problems, so I won't be audacious and claim that I have 'the' proof; however, I have been able to convince myself and a few other people with graduate level training in mathematics that this solution is true.
I have...