V2EX nullspace

Nullspace

释义 Definition

零空间 / 核(kernel):在线性代数中,对给定矩阵 \(A\),所有满足 \(A\mathbf{x}= \mathbf{0}\) 的向量 \(\mathbf{x}\) 构成的集合。它是一个向量空间,反映矩阵把哪些向量“压扁”为零向量。(在一些语境下也可写作 null space。)

发音 Pronunciation

/nlspes/

例句 Examples

The nullspace of this matrix contains all vectors that it sends to zero.
这个矩阵的零空间包含所有被它映射为零向量的向量。

To determine whether the system has nontrivial solutions, we compute the nullspace and examine its dimension.
为了判断该方程组是否存在非零解,我们计算零空间并考察其维数。

词源 Etymology

null- 来自拉丁语 nullus(“没有、零”),表示“为空/为零”;space 指“空间/集合”。合起来表示“映到零的向量所构成的空间”。在线性代数里也常用同义术语 kernel(核)

相关词 Related Words

文学与著名作品 Literary Works

“nullspace”更常见于数学教材与学术写作中,较少作为文学作品的高频词汇;在经典线性代数教材中常出现,例如:

  • Linear Algebra and Its Applications(David C. Lay)
  • Introduction to Linear Algebra(Gilbert Strang)
  • Linear Algebra(Serge Lang)
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