不變子空間亦稱穩定子空間,又稱平凡子空間,與線性變換有關的一種子空間。設σ是數域P上線性空間V的線性變換,W是V的子空間,若對W中的任意一個向量α,σ(α)也屬於W,則稱W是σ的不變子空間或稱σ子空間。σ的值域與核以及σ的特徵子空間等都是σ的不變子空間,有限維的複線性空間的所有的線性變換都有一維不變子空間,有限維實線性空間的線性變換都有一維或二維不變子空間,特別地,奇數維的實線性空間的每一個線性變換都有一維的不變子空間。
基本介紹
- 中文名:不變子空間
- 外文名:Invariant subspace
- 別名:穩定子空間、平凡子空間
- 特點:與線性變換有關的一種子空間
定義
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定理
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例題
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