Re: A letter want to disprove my paper which submitted recently



Hi Zhu, I read your paper, and it is very interesting.

On page 8 of your article on "http://arxiv.org/PS_cache/arxiv/pdf/
0704/0704.0309v2.pdf", first line, you have mentioned that complexity
of calculating the rank of a matrix is O(N^3). As the complexities of
all other subsets of your Algorithm are lesser than O(N^3), so
therefore you have concluded that overall complexity of your Algorithm
= O (N^3).

Can u please indicate some papers or references, which say that
calculating the rank of a matrix is O(N^3) ?

So far, I thought that calculating the rank of a Generic matrix within
polynomial time, is an unsolved OPEN problem.

One famous paper which states that this is an OPEN problem is
Yannakakis paper (see last paragraph of the paper) - "Expressing
combinatorial optimization problems by linear programs".

.



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