In
mathematics, a Sylvester domain, named after
James Joseph Sylvester by , is a
ring
Ring may refer to:
* Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry
* To make a sound with a bell, and the sound made by a bell
:(hence) to initiate a telephone connection
Arts, entertainment and media Film and ...
in which Sylvester's law of nullity holds. This means that if ''A'' is an ''m'' by ''n''
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** ''The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
, and ''B'' is an ''n'' by ''s'' matrix over ''R'', then
:ρ(''AB'') ≥ ρ(''A'') + ρ(''B'') – ''n''
where ρ is the inner rank of a matrix. The inner rank of an ''m'' by ''n'' matrix is the smallest integer ''r'' such that the matrix is a product of an ''m'' by ''r'' matrix and an ''r'' by ''n'' matrix.
showed that
fields
Fields may refer to:
Music
* Fields (band), an indie rock band formed in 2006
* Fields (progressive rock band), a progressive rock band formed in 1971
* ''Fields'' (album), an LP by Swedish-based indie rock band Junip (2010)
* "Fields", a song b ...
satisfy Sylvester's law of nullity and are, therefore, Sylvester domains.
References
*
*
Ring theory
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