norm：翻译为模或者内积，广义来说是一个函数
vector（向量） norms
1. eculidean（欧几里得）norm
vector (x = (x_1;x_2; ...; x_n))
其eculidean norm为 ：(||x|| = sqrt{x^T x} = (sum_{i=1}^n x_i^2)^{frac 12} = sqrt{x_1^2 +x_2^2 + ...+x_n^2})
2. P norm (P>=1)
[||x||_p = (sum_{i=1}^n {|x_i|}^p)^{frac 1p}
]
常用：1 norm 、2norm（eculidean norm）、(infty) norm
matrix norms
there have a matrix A (in C^{m imes n})
1. frobenius matrix norm (F norm)
[||x||_F^2 = sum_{ij}{|a_{ij}|}^2 = sum_i {||A_{i*}||}_2^2 =sum_j {||A_{*j}||}_2^2 = trace(A^* A)
]
2. matrix 2-norm
[||A||_2 = sqrt {lambda_{max}}
]
[lambda_{max} quad {是A^* A 最大特征值}
]
3. matrix 1-norm
[||A||_1 = \, {列向量最大1模}
]
4. matrix (infty) norm
[||A||_{infty} =\, {行向量最大1模}
]