V2EX commutativity

Commutativity

释义 Definition

可交换性;交换律性质:在数学中指某种运算中,改变运算对象的顺序,结果不变。最常见的例子是加法与乘法:\(a+b=b+a\),\(ab=ba\)。
(在更高等的代数结构中,也可指某个运算或结构“满足交换律”的性质。)

发音 Pronunciation (IPA)

/kmjuttvti/

例句 Examples

Addition has commutativity: 3 + 5 equals 5 + 3.
加法具有可交换性:3 + 5 等于 5 + 3。

In matrix multiplication, commutativity usually fails, which is why AB may not equal BA.
在矩阵乘法中,可交换性通常不成立,这也是为什么 AB 未必等于 BA。

词源 Etymology

commutativity 来自 commute(交换、互换)与后缀 -ivity(表示“性质、状态”)。其更早可追溯到拉丁语 commutare,意为“互换、改变”,其中 com- 表示“一起、共同”,mutare 表示“改变”。因此该词字面意思就是“可以互相交换的性质”。

相关词 Related Words

文学与著作 Literary Works

  • A Survey of Modern Algebra(Garrett Birkhoff, Saunders Mac Lane):讨论代数结构时频繁使用“commutativity/commutative”来刻画交换律相关性质。
  • Abstract Algebra(David S. Dummit, Richard M. Foote):在群、环、域等章节中用该词描述运算满足交换律的性质。
  • Linear Algebra Done Right(Sheldon Axler):在讨论线性变换、矩阵与算子时,会强调某些运算“不具有 commutativity”。
关于     帮助文档     自助推广系统     博客     API     FAQ     Solana     1908 人在线   最高记录 6679       Select Language
创意工作者们的社区
World is powered by solitude
VERSION: 3.9.8.5 7ms UTC 05:41 PVG 13:41 LAX 21:41 JFK 00:41
Do have faith in what you're doing.
ubao msn snddm index pchome yahoo rakuten mypaper meadowduck bidyahoo youbao zxmzxm asda bnvcg cvbfg dfscv mmhjk xxddc yybgb zznbn ccubao uaitu acv GXCV ET GDG YH FG BCVB FJFH CBRE CBC GDG ET54 WRWR RWER WREW WRWER RWER SDG EW SF DSFSF fbbs ubao fhd dfg ewr dg df ewwr ewwr et ruyut utut dfg fgd gdfgt etg dfgt dfgd ert4 gd fgg wr 235 wer3 we vsdf sdf gdf ert xcv sdf rwer hfd dfg cvb rwf afb dfh jgh bmn lgh rty gfds cxv xcv xcs vdas fdf fgd cv sdf tert sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf shasha9178 shasha9178 shasha9178 shasha9178 shasha9178 liflif2 liflif2 liflif2 liflif2 liflif2 liblib3 liblib3 liblib3 liblib3 liblib3 zhazha444 zhazha444 zhazha444 zhazha444 zhazha444 dende5 dende denden denden2 denden21 fenfen9 fenf619 fen619 fenfe9 fe619 sdf sdf sdf sdf sdf zhazh90 zhazh0 zhaa50 zha90 zh590 zho zhoz zhozh zhozho zhozho2 lislis lls95 lili95 lils5 liss9 sdf0ty987 sdft876 sdft9876 sdf09876 sd0t9876 sdf0ty98 sdf0976 sdf0ty986 sdf0ty96 sdf0t76 sdf0876 df0ty98 sf0t876 sd0ty76 sdy76 sdf76 sdf0t76 sdf0ty9 sdf0ty98 sdf0ty987 sdf0ty98 sdf6676 sdf876 sd876 sd876 sdf6 sdf6 sdf9876 sdf0t sdf06 sdf0ty9776 sdf0ty9776 sdf0ty76 sdf8876 sdf0t sd6 sdf06 s688876 sd688 sdf86