1 Vector Spaces
目录
1.14 Norms of Linear Transformation
1.5 Affine Sets
- affine set: , holds.
- aff(S): for a set , aff(S) is the intersection of affine sets containing S.Clearly, it is the smallest affine set that containing S.
- hypeplane: ,
- half-spaces: ,
1.7 The Space
- Q-inner product :
- norm of vector: p-范数: -范数:
- norm of martix: 列范数: 行范数: 2-范数: 21-范数: (每行2-范数求和)
1.7.1 Subsets of (注)
- nongegative orthant: (向量元素都大于等于0的)
- positive orthant: (向量元素都大于0的)
- unit simplex: (向量元素都大于等于0的且和为1的)
1.8 The Space
1.8.2 Norms in
- Frobenius norm:
- (a, b)-norm:
1.10 Linear Transforamtions
- linear-transformation:
1.11 The Dual Space
- linear functional:
- dual space : all linear functional on
- dual norm:
- generalized Cauchy-Schwars inequlity:
- 向量范数对偶:需满足,如 1与范数,2范数本身
- 矩阵范数对偶:谱范数-核范数(特征值之和)
1.13 Adjoint Transformations
1.14 Norms of Linear Transformation