Normal forms: Difference between revisions
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# If ''k'' > ''F'' (''i'') > 0 then H[''k'', ''i''] = 0; that is, ''F'' (''i'') is the row of the first nonzero entry in the ''i''-th column, counting up from the bottom. | # If ''k'' > ''F'' (''i'') > 0 then H[''k'', ''i''] = 0; that is, ''F'' (''i'') is the row of the first nonzero entry in the ''i''-th column, counting up from the bottom. | ||
# If ''F'' (''i'') > 0 then H[''F'' (''i''), ''i''] > 0; that is, the first nonzero entry in the ''i''-th column, counting up from the bottom, is positive. | # If ''F'' (''i'') > 0 then H[''F'' (''i''), ''i''] > 0; that is, the first nonzero entry in the ''i''-th column, counting up from the bottom, is positive. | ||
# If ''F'' (''i'') > 0 and ''i'' < ''j'' then H[''F'' (''i''), ''i''] > H[F(''i''), ''j''] ≥ 0; that is, the first nonzero entry in the ''i''-th column, counting up from the bottom, is greater than any of the rest along that row, which however are all non-negative. | # If ''F'' (''i'') > 0 and ''i'' < ''j'' then H[''F'' (''i''), ''i''] > H[''F'' (''i''), ''j''] ≥ 0; that is, the first nonzero entry in the ''i''-th column, counting up from the bottom, is greater than any of the rest along that row, which however are all non-negative. | ||
There is some redundancy in the statement of these conditions, but that does no harm. | There is some redundancy in the statement of these conditions, but that does no harm. | ||