V2EX sesquilinear

Sesquilinear

Definition / 定义

(数学)半双线性的;半线性的:指一个函数/形式对两个自变量“几乎都线性”,通常是对一个变量线性,而对另一个变量共轭线性(在复数向量空间中常见),如“sesquilinear form(半双线性形式)”。

Pronunciation / 发音

/sskwlni/

Examples / 例句

A sesquilinear form is common in complex inner product spaces.
半双线性形式在复内积空间中很常见。

Let \(B(x,y)\) be sesquilinear, linear in \(x\) and conjugate-linear in \(y\), so that \(B(x,ay)=\overline{a}\,B(x,y)\).
设 \(B(x,y)\) 为半双线性的,对 \(x\) 线性、对 \(y\) 共轭线性,因此 \(B(x,ay)=\overline{a}\,B(x,y)\)。

Etymology / 词源

来自拉丁语前缀 sesqui-(意为“一个半、一次半”)+ linear(“线性的”)。在数学里用来表达“比双线性少一点、介于线性与双线性之间”的感觉:一边线性,另一边带共轭的线性

Related Words / 相关词

Literary Works / 文学与著作例

  • Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis(Reed & Simon)讨论半双线性形式与内积结构
  • Functional Analysis(Walter Rudin)在Hilbert空间/算子理论语境中使用“sesquilinear form”
  • Linear Operators, Part I(Dunford & Schwartz)涉及半双线性形式与相关泛函分析概念
  • A Course in Functional Analysis(John B. Conway)在内积与算子章节中出现该术语
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