V2EX noninvertible

Noninvertible

定义 Definition

noninvertible(形容词):(在数学/线性代数中)不可逆的;指一个函数、矩阵或变换没有逆,无法“反过来”唯一地恢复输入(常见于奇异矩阵非一一对应的映射)。在不同语境中也可泛指“无法逆转/不可恢复”的过程,但最常见用法是数学意义。

发音 Pronunciation (IPA)

/nn nvrtbl/(英式)
/nn nvtbl/(美式)

例句 Examples

This matrix is noninvertible.
这个矩阵是不可逆的。

Because the transformation is noninvertible, multiple inputs can produce the same output, so the original data cannot be uniquely recovered.
由于这个变换不可逆,多个输入可能得到同一个输出,因此无法唯一地恢复原始数据。

词源 Etymology

由前缀 non-(“不、非”)+ invertible(“可逆的”)构成。invertible 源自拉丁语 invertere(“翻转、颠倒”),在数学语境中引申为“能否通过逆运算回到原状”。加上 non- 后即表示“不能通过逆运算恢复”的性质。

相关词 Related Words

文学与著作 Literary Works

  • Linear Algebra Done Right(Sheldon Axler)
  • Introduction to Linear Algebra(Gilbert Strang)
  • Linear Algebra(Serge Lang)
  • Matrix Analysis(Roger A. Horn & Charles R. Johnson)
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