Normal forms: Difference between revisions
Cmloegcmluin (talk | contribs) add back IRREF on Kite's request |
m →IRREF: correction. The minimal ratio form doesn't use HNF either |
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Another important normalized form for integer matrices is what [[Kite Giedraitis]] has dubbed the IRREF, the '''integer reduced row echelon form'''. It is the [[Wikipedia: Row echelon form|reduced row echelon form]] but with integer entries, found by multiplying each row of the matrix by the least common multiple of all denominators in that row. It differs from the Hermite normal form in that each pivot is the only nonzero entry in its column. For a monzo list, it has the advantage of limiting the appearance of the ''N'' highest primes to only one comma each (where ''N'' is the codimension), isolating each prime's effect on the [[pergen]], but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion. | Another important normalized form for integer matrices is what [[Kite Giedraitis]] has dubbed the IRREF, the '''integer reduced row echelon form'''. It is the [[Wikipedia: Row echelon form|reduced row echelon form]] but with integer entries, found by multiplying each row of the matrix by the least common multiple of all denominators in that row. It differs from the Hermite normal form in that each pivot is the only nonzero entry in its column. For a monzo list, it has the advantage of limiting the appearance of the ''N'' highest primes to only one comma each (where ''N'' is the codimension), isolating each prime's effect on the [[pergen]], but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion. | ||
This | This form and the minimal ratio form are the only forms on this page which does not use the HNF, although sometimes the IRREF is identical to the HNF. For more information, see [[IRREF]]. | ||
== Maple code == | == Maple code == | ||