Projection matrices: Difference between revisions

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===Algebraic considerations===

For the mathematically inclined (other people may want to skip this paragraph) we note that monzos are elements of a [[Stacking|free abelian group]] (or equivalently, Z-module) of rank ''n'' equal to the number of primes less than or equal to ''p'' for the ''p''-limit in question. Fractional monzos do not define a free group but rather a [[Wikipedia:Divisible group|divisible group]], meaning any element may be divided by any nonzero integer. They are Z-modules, but more than that also Q-modules, or stated equivalently, elements in a [[Wikipedia:Vector space|vector space]] (of dimension ''n'') over the rational numbers. They are also torsion-free (equivalently, [[Wikipedia:Flat module|flat]]) abelian groups, and are the [[Wikipedia:Injective hull|injective hulls]] of the corresponding monzos.

=== See also ===

* [[Projection]]: an introduction to the topic

@@ Line 24: / Line 24: @@
 ===Algebraic considerations===
 For the mathematically inclined (other people may want to skip this paragraph) we note that monzos are elements of a [[Stacking|free abelian group]] (or equivalently, Z-module) of rank ''n'' equal to the number of primes less than or equal to ''p'' for the ''p''-limit in question. Fractional monzos do not define a free group but rather a [[Wikipedia:Divisible group|divisible group]], meaning any element may be divided by any nonzero integer. They are Z-modules, but more than that also Q-modules, or stated equivalently, elements in a [[Wikipedia:Vector space|vector space]] (of dimension ''n'') over the rational numbers. They are also torsion-free (equivalently, [[Wikipedia:Flat module|flat]]) abelian groups, and are the [[Wikipedia:Injective hull|injective hulls]] of the corresponding monzos.
+=== See also ===
+* [[Projection]]: an introduction to the topic