谱半径
Multi tool use
矩阵谱半径
定义
设A是n × n矩阵，λ1, ..., λn是其特征值，則A的谱半径ρ(A)定義如下：
ρ(A)=max{|λ1|,⋯,|λn|}.{displaystyle rho (A)=max left{|lambda _{1}|,cdots ,|lambda _{n}|right}.}
即矩阵A的谱半径等于矩阵A的特征值绝对值的最大值。
泛函分析
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| 集合 / 子集 |
- 绝对凸集
- 吸收集
- 平衡集
- 有界集 (拓扑向量空间)
- 凸集
- 径向集
- 星形域
- 对称集
- 凸锥
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| 拓扑向量空间 |
- 巴拿赫空间
- 欧几里得空间
- 希尔伯特空间
- 局部凸
赋范向量空间 (范数)
- 拟赋范空间
- 自反空间
拓扑张量积 (希尔伯特空间中)
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| 映射拓扑 |
- 对偶空间
- 算子拓扑
- 弱拓扑
- 强拓扑
- 拓扑的一致收敛
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| 线性算子 |
- 伴随
双线性映射 (双线性型)
有界算子 / 无界算子
- 连续线性算子
- 紧算子
- Fredholm算子
- 希尔伯特-施密特算子
- 线性泛函
- 正规算子
- 核型算子
- 自伴算子
- 严格奇异算子
- 迹类算子
- 线性映射转置
- 酉算子
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| 集合运算 |
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| 算子理论 |
- 巴拿赫代数
- C*-代数
谱 (泛函分析) (谱半径)
谱理论(谱定理)
- 极分解
- 奇异值分解
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| 定理 |
- 阿尔泽拉－阿斯科利定理
- 巴拿赫-阿劳格鲁定理
- 巴拿赫-马祖尔定理
- 贝尔纲定理
- 贝塞尔不等式
- 柯西-施瓦茨不等式
- 闭值域定理
- 闭图像定理
- 哈恩－巴拿赫定理
- 角谷不动点定理
- 不变子空间问题
- Riesz延拓定理
- 开映射定理
- 拉克斯－米尔格拉姆定理
- 帕塞瓦尔恒等式
- 肖德尔不动点定理
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| 分析 |
导数 (加托导数
泛函导数)
积分 (博赫纳积分
佩蒂斯积分)
泛函演算 (波莱尔泛函演算
连续泛函演算)
- 反函数定理
- 向量测度
- 弱可测函数
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