V2EX system of equations

System of Equations

Definition / 释义

“system of equations” 指“一组方程(方程组)”,通常包含两个或以上方程,用来同时求解同一组未知数;常见于代数、线性代数与应用数学中。(也可泛指非线性方程组。)

Pronunciation / 发音(IPA)

/sstm v kwenz/

Examples / 例句

Solve the system of equations to find x and y.
解这个方程组来求出 x 和 y。

In physics, a system of equations can model how multiple variables interact, and small changes in one equation may affect the entire solution.
在物理学中,方程组可以用来刻画多个变量如何相互作用,而其中一个方程的微小变化可能会影响整体解。

Etymology / 词源

system 源自希腊语 systēma,意为“组合在一起的整体、体系”;equation 源自拉丁语 aequatio,与 aequus(“相等的”)相关。合起来表示“由多个‘相等关系’构成的整体”,即“方程的体系/集合”。

Related Words / 相关词汇

Literary Works / 文献与作品中的用例

  • Introduction to Linear Algebra(Gilbert Strang)大量使用并讲解线性方程组及其矩阵表示。
  • Linear Algebra Done Right(Sheldon Axler)以线性系统、线性变换等概念贯穿线性代数。
  • A First Course in Abstract Algebra(John B. Fraleigh)在相关章节中讨论方程组与代数结构的联系。
  • Principia Mathematica(Whitehead & Russell)在形式化推理与符号体系讨论中涉及“方程/方程组”类表达。
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