V2EX square matrix

Square Matrix

释义 Definition

方阵:行数与列数相同的矩阵(即 n × n 矩阵)。在线性代数中,方阵常用于描述线性变换、求行列式、特征值与特征向量等。(该词在某些语境下也可泛指“正方形网格/矩阵结构”,但最常见的是数学含义。)

发音 Pronunciation (IPA)

/skwr metrks/

例句 Examples

A 2×2 square matrix has two rows and two columns.
一个 2×2 的方阵有两行两列。

If a square matrix is invertible, its determinant is nonzero and the linear system has a unique solution.
如果一个方阵可逆,那么它的行列式不为零,并且该线性方程组有唯一解。

词源 Etymology

square 原意与“方形、成直角”相关,来自古法语 esquarre(与“角尺/直角”有关),再追溯到拉丁语 exquadra 一类的形式。matrix 来自拉丁语 matrix,意为“母体/子宫”,在数学中引申为“承载并生成结构的数据表/框架”。合起来 square matrix 就是“呈正方形结构(行列相等)的矩阵”。

相关词 Related Words

文学与名著用例 Literary Works

  • Introduction to Linear Algebra Gilbert Strang(大量使用“square matrix”讨论行列式、特征值等)
  • Linear Algebra Done Right Sheldon Axler(围绕方阵与线性算子展开,常出现该术语)
  • Linear Algebra Serge Lang(经典教材,方阵是核心对象之一)
  • Matrix Analysis Roger A. Horn & Charles R. Johnson(矩阵分析名著,广泛涉及方阵性质)
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