This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

라이선스가 부여된 사용자만 번역 문서를 볼 수 있습니다. 번역 문서를 보려면 로그인하십시오.


Vector and matrix norms




n = norm(v) returns the 2-norm or Euclidean norm of vector v.


n = norm(v,p) returns the vector norm defined by sum(abs(v)^p)^(1/p), where p is any positive real value, Inf, or -Inf.

  • If p is Inf, then n = max(abs(v)).

  • If p is -Inf, then n = min(abs(v)).


n = norm(X) returns the 2-norm or maximum singular value of matrix X.


n = norm(X,p) returns the p-norm of matrix X, where p is 1, 2, or Inf.


n = norm(X,'fro') returns the Frobenius norm, sqrt(sum(diag(X'*X))).


collapse all

Calculate the 2-norm of a vector corresponding to the point (-2,3,-1) in 3-D space. The 2-norm is equal to the Euclidean length of the vector.

X = [-2 3 -1];
n = norm(X)
n =


Calculate the 1-norm of the vector, which is the sum of the element magnitudes.

n = norm(X,1)
n =


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 =


Use 'fro' to calculate the Frobenius norm of a sparse matrix, which calculates the 2-norm of the column vector, S(:).

S = sparse(1:25,1:25,1);
n = norm(S,'fro')
n =


Input Arguments

collapse all

Input vector.

Data Types: single | double
Complex Number Support: Yes

Input matrix. Use norm(X,'fro') when X is sparse.

Data Types: single | double
Complex Number Support: Yes

Norm type, specified as 2 (default), a different positive integer scalar, Inf, or -Inf. The valid values of p and what they return depend on whether the first input to norm is a matrix or vector, as shown in the table.

    Note:   This table does not reflect the actual algorithms used in calculations.

Positive, real-valued numeric psum(abs(X).^p)^(1/p)

Output Arguments

collapse all

Matrix or vector norm, returned as a scalar. The norm gives a measure of the magnitude of the elements. By convention, norm returns NaN if the input contains NaN values.

More About

collapse all

Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.

See Also

| | | |

Introduced before R2006a

Was this topic helpful?