## numpy.linalg.norm#

This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter.

Parameters : **x** array_like

Input array. If *axis* is None, *x* must be 1-D or 2-D, unless *ord* is None. If both *axis* and *ord* are None, the 2-norm of x.ravel will be returned.

Order of the norm (see table under Notes ). inf means numpy’s inf object. The default is None.

If *axis* is an integer, it specifies the axis of *x* along which to compute the vector norms. If *axis* is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. If *axis* is None then either a vector norm (when *x* is 1-D) or a matrix norm (when *x* is 2-D) is returned. The default is None.

New in version 1.8.0.

If this is set to True, the axes which are normed over are left in the result as dimensions with size one. With this option the result will broadcast correctly against the original *x*.

New in version 1.10.0.

Norm of the matrix or vector(s).

Similar function in SciPy.

For values of ord < 1 , the result is, strictly speaking, not a mathematical ‘norm’, but it may still be useful for various numerical purposes.

## numpy.linalg.norm¶

This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter.

**x** : array_like

Input array. If *axis* is None, *x* must be 1-D or 2-D.

Order of the norm (see table under Notes ). inf means numpy’s *inf* object.

If *axis* is an integer, it specifies the axis of *x* along which to compute the vector norms. If *axis* is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. If *axis* is None then either a vector norm (when *x* is 1-D) or a matrix norm (when *x* is 2-D) is returned.

**keepdims** : bool, optional

If this is set to True, the axes which are normed over are left in the result as dimensions with size one. With this option the result will broadcast correctly against the original *x*.

New in version 1.10.0.

**n** : float or ndarray

Norm of the matrix or vector(s).

For values of ord <= 0 , the result is, strictly speaking, not a mathematical ‘norm’, but it may still be useful for various numerical purposes.

The following norms can be calculated:

ord | norm for matrices | norm for vectors |
---|---|---|

None | Frobenius norm | 2-norm |

‘fro’ | Frobenius norm | – |

‘nuc’ | nuclear norm | – |

inf | max(sum(abs(x), axis=1)) | max(abs(x)) |

-inf | min(sum(abs(x), axis=1)) | min(abs(x)) |

0 | – | sum(x != 0) |

1 | max(sum(abs(x), axis=0)) | as below |

-1 | min(sum(abs(x), axis=0)) | as below |

2 | 2-norm (largest sing. value) | as below |

-2 | smallest singular value | as below |

other | – | sum(abs(x)**ord)**(1./ord) |

The Frobenius norm is given by [R46]: