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In mathematics, a Sylvester domain, named after James Joseph Sylvester by , is a ring in which Sylvester's law of nullity holds. This means that if ''A'' is an ''m'' by ''n'' matrix and ''B'' 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 satisfy Sylvester's law of nullity and are therefore Sylvester domains. ==References== * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sylvester domain」の詳細全文を読む スポンサード リンク
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