V2EX augmented matrix

Augmented Matrix

释义 Definition(中文)

增广矩阵:在线性代数中,把线性方程组的系数矩阵与等号右边的常数项(或额外信息)按列拼接在一起形成的矩阵,常写作 \([A \mid b]\) 或 \([A \mid B]\)。常用于高斯消元、判断方程组是否有解及求解。

发音 Pronunciation(IPA)

/mntd metrks/

例句 Examples

Write the system as an augmented matrix before solving it.
在求解之前,把这个方程组写成增广矩阵。

By applying Gaussian elimination to the augmented matrix, we can determine whether the linear system has a unique solution.
通过对增广矩阵进行高斯消元,我们可以判断这个线性方程组是否有唯一解。

词源 Etymology(中文)

augmented 来自拉丁语 augmentare(“增加、扩充”),表示“被加上去的/扩充后的”;matrix 来自拉丁语 matrix(“母体、来源”),在数学里引申为“矩阵”。合起来,augmented matrix 字面就是“被扩充的矩阵”,指在原系数矩阵旁边增添一列或多列(常数列或其他列)以便运算与分析。

相关词 Related Words

  • Matrix
  • Coefficient Matrix
  • Linear System
  • Gaussian Elimination
  • Row Reduction
  • Reduced Row Echelon Form
  • Rank
  • Consistency
  • 文学与著作 Literary Works(出现来源示例)

    • Introduction to Linear Algebra(Gilbert Strang)
    • Linear Algebra and Its Applications(David C. Lay, Steven R. Lay, Judi J. McDonald)
    • Linear Algebra Done Right(Sheldon Axler)
    • Elementary Linear Algebra(Howard Anton 等)
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