格式
n = norm(A);
n = norm(A,p);
功能描述
The norm of a matrix is a scalar that gives some measure of the magnitude of the elements of the matrix. The norm function calculates several different types of matrix norms:
n = norm(A) returns the largest singular value of A, max(svd(A)).
n = norm(A,p) returns a different kind of norm, depending on the value of p.
| if p is... | The norm return ... |
| 1 | The 1-norm, or largest column sum of A, max(sum(abs(A)) |
| 2 | The largest singular value (same as norm(A)) |
| inf | The infinity norm, or largest row sum of A, max(sum(abs(A'))) |
| ' fro ' | The Frobenius-norm of matrix A, sqrt(sum(diag(A'*A))) |
When A is a vector:
norm(A,p)Returns sum(abs(A).^p)^(1/p), for any 1 <= p <= .
norm(A)Returns norm(A,2).
norm(A,inf)Returns max(abs(A)).
norm(A,-inf)Returns min(abs(A)).
1、如果A為矩陣
n=norm(A)
返回A的最大奇異值，即max(svd(A))
n=norm(A,p)
根據p的不同，返回不同的值
| p值 | 返回值 |
| 1 | 返回A中最大一列和，即max(sum(abs(A))) |
| 2 | 返回A的最大奇異值，和n=norm(A)用法一樣 |
| inf | 返回A中最大一行和，即max(sum(abs(A’))) |
| ‘fro’ | A和A‘的積的對角線和的平方根，即sqrt(sum(diag(A'*A))) |
2、如果A為向量
norm(A,p)
返回向量A的p範數。即返回 sum(abs(A).^p)^(1/p),對任意 1<p<+∞.
norm(A)
返回向量A的2範數，即等價於norm(A,2)。
norm(A,inf)
返回max(abs(A))
norm(A,-inf)
返回min(abs(A))
實例
x = [0 1 2 3]
x =
0 1 2 3
sqrt(0+1+4+9) % Euclidean length
ans =
3.7417
norm(x)
ans =
3.7417
n = length(x) % Number of elements
n =
4
rms = 3.7417/2 % rms = norm(x)/sqrt(n)
rms =
1.8708
