norm
Vector and matrix norms
Syntax
n = norm(v)
n = norm(v,p)
n = norm(X)
n = norm(X,p)
n = norm(X,'fro')
Description
n = norm（v）返回向量v的欧几里德范数。该范数也称为2范数，向量幅度或欧几里德长度。
n = norm（v，p）返回广义向量p范数。
n = norm（X）返回矩阵X的2范数或最大奇异值，其近似为max（svd（X））。
n = norm（X，p）返回矩阵X的p范数，其中p为1,2或Inf：
- 如果p = 1，则n是矩阵的最大绝对列和。
- 如果p = 2，则n近似为max（svd（X））。 这相当于norm（X）。
- 如果p = Inf，那么n是矩阵的最大绝对行和。
n = norm（X，'fro'）返回矩阵X的Frobenius范数。
有关范数的基础知识，见博文：【 MATLAB 】范数的必备基础知识
下面举例说明：
Vector Magnitude（向量幅度）
%Create a vector and calculate the magnitude.
v = [1 -2 3];
n = norm(v)
% n = 3.7417
1-Norm of Vector
clc
clear
close all
% Calculate the 1-norm of a vector, which is the sum of the element magnitudes.
X = [-2 3 -1];
n = norm(X,1)
% n = 6
Euclidean Distance Between Two Points
clc
clear
close all
% Calculate the distance between two points as the norm of the difference between the vector elements.
%
% Create two vectors representing the (x,y) coordinates for two points on the Euclidean plane.
a = [0 3];
b = [-2 1];
% Use norm to calculate the distance between the points.
d = norm(b-a)
d =
2.8284
几何上，两点之间的距离：
2-Norm of Matrix
clc
clear
close all
% Calculate the 2-norm of a matrix, which is the largest singular value.
X = [2 0 1;-1 1 0;-3 3 0];
n = norm(X)
% n = 4.7234
Frobenius Norm of Sparse Matrix
clc
clear
close all
% 使用'fro'计算稀疏矩阵的Frobenius范数，该范数计算列向量的2范数S（:)。
S = sparse(1:25,1:25,1);
n = norm(S,'fro')
% n = 5
