V2EX coefficient matrix

Coefficient Matrix

Definition / 释义

coefficient matrix(系数矩阵):在线性方程组中,由各个方程里未知数前的系数按一定顺序排列成的矩阵(通常不包含常数项)。常与“增广矩阵(augmented matrix)”相对。

Pronunciation / 发音(IPA)

/kofnt metrks/

Examples / 例句

The coefficient matrix is singular, so the system may have infinitely many solutions.
系数矩阵是奇异的,因此这个方程组可能有无穷多解。

By row-reducing the coefficient matrix, we can determine whether the linear system is consistent and find its solution set.
通过对系数矩阵做行化简,我们可以判断线性方程组是否相容,并求出它的解集。

Etymology / 词源

coefficient 来自拉丁语 *co-*(共同)+ efficere(完成、产生效果),在数学里引申为“与未知量相乘、共同决定结果的数”,即“系数”。matrix 原义与“母体/孕育之处”有关,后来在数学中用来表示“数的排列结构”。合在一起,coefficient matrix 就是“由系数组成的矩阵”。

Related Words / 相关词

Notable Works / 文献与著作中的用例

  • Introduction to Linear Algebra(Gilbert Strang,《线性代数导论》)
  • Linear Algebra Done Right(Sheldon Axler,《线性代数应该这样学》)
  • Linear Algebra(Serge Lang,《线性代数》)
  • Finite-Dimensional Vector Spaces(Paul R. Halmos,《有限维向量空间》)
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