I am working with a semi-positive 413 x 413 input-output table from the Bureau of Economic Analysis.When I use the default precision in MathCad 14, I get that the rank is 410 and I find that there are indeed only 410 nonzero eigenvalues (i.e. the last three of 413 calculated eigenvalues are zero).
However, when I increase the precision of the result, the last three eigenvalues come in as nonzero, on the order of E-17 and E-18. Nonetheless the rank remains at 410 even when I increase the precision to E-300. So now I have an apparent contradiction: a full complement of eigenvalues (413) which implies a rank of 413: and a calculated rank which is stubbornly at 410. Which one of these contradictory results should I trust?
The matrix in question is attached as a .csv file. Any help would be greatly appreciated.
Anwar .
