V2EX zero matrix

Zero Matrix

定义 Definition

零矩阵:所有元素都为 0 的矩阵,通常记作 0 或 **0_{m×n}**。它在矩阵加法中起到“加法单位元”的作用:任意矩阵 \(A\) 都满足 \(A + 0 = A\)。在矩阵乘法中,与任何相容矩阵相乘通常得到零矩阵:\(A0 = 0\)、\(0A = 0\)。

发音 Pronunciation (IPA)

/zro metrks/

例句 Examples

The zero matrix has all entries equal to 0.
零矩阵的所有元素都等于 0。

If \(A\) is any \(m \times n\) matrix, then \(A + 0_{m\times n} = A\), and multiplying by a compatible zero matrix gives the zero matrix.
如果 \(A\) 是任意 \(m \times n\) 矩阵,那么 \(A + 0_{m\times n} = A\),并且与维度相容的零矩阵相乘会得到零矩阵。

词源 Etymology

zero 来自意大利语 zero(“零”),更早可追溯到阿拉伯语 ifr(“空、无”),也影响了英语 cipher 的来源;matrix 来自拉丁语 matrix(“母体、源头”),在数学中借用来表示“元素的排列/容器”。合起来 zero matrix 就是“元素全为零的矩阵”。

相关词 Related Words

  • Null Matrix
  • Matrix
  • Zero Vector
  • Identity Matrix
  • Scalar
  • Additive Identity
  • Linear Transformation
  • Rank
  • 文学与经典作品 Literary Works

    • Gilbert Strang, Introduction to Linear Algebra(《线性代数导论》)
    • Sheldon Axler, Linear Algebra Done Right(《线性代数应该这样学》)
    • Kenneth Hoffman & Ray Kunze, Linear Algebra(《线性代数》)
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