# tf.norm

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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.13.1/tensorflow/python/ops/linalg_ops.py#L557-L625) |

Computes the norm of vectors, matrices, and tensors.

#### View aliases


**Main aliases**

[`tf.linalg.norm`](https://www.tensorflow.org/api_docs/python/tf/norm)

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    tf.norm(
        tensor, ord='euclidean', axis=None, keepdims=None, name=None
    )

This function can compute several different vector norms (the 1-norm, the
Euclidean or 2-norm, the inf-norm, and in general the p-norm for p \> 0) and
matrix norms (Frobenius, 1-norm, 2-norm and inf-norm).

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| ## Args ||
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| `tensor` | `Tensor` of types `float32`, `float64`, `complex64`, `complex128` |
| `ord` | Order of the norm. Supported values are `'fro'`, `'euclidean'`, `1`, `2`, `np.inf` and any positive real number yielding the corresponding p-norm. Default is `'euclidean'` which is equivalent to Frobenius norm if `tensor` is a matrix and equivalent to 2-norm for vectors. Some restrictions apply: a) The Frobenius norm `'fro'` is not defined for vectors, b) If axis is a 2-tuple (matrix norm), only `'euclidean'`, '`fro'`, `1`, `2`, `np.inf` are supported. See the description of `axis` on how to compute norms for a batch of vectors or matrices stored in a tensor. |
| `axis` | If `axis` is `None` (the default), the input is considered a vector and a single vector norm is computed over the entire set of values in the tensor, i.e. `norm(tensor, ord=ord)` is equivalent to `norm(reshape(tensor, [-1]), ord=ord)`. If `axis` is a Python integer, the input is considered a batch of vectors, and `axis` determines the axis in `tensor` over which to compute vector norms. If `axis` is a 2-tuple of Python integers it is considered a batch of matrices and `axis` determines the axes in `tensor` over which to compute a matrix norm. Negative indices are supported. Example: If you are passing a tensor that can be either a matrix or a batch of matrices at runtime, pass `axis=[-2,-1]` instead of `axis=None` to make sure that matrix norms are computed. |
| `keepdims` | If True, the axis indicated in `axis` are kept with size 1. Otherwise, the dimensions in `axis` are removed from the output shape. |
| `name` | The name of the op. |

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| ## Returns ||
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| `output` | A `Tensor` of the same type as tensor, containing the vector or matrix norms. If `keepdims` is True then the rank of output is equal to the rank of `tensor`. Otherwise, if `axis` is none the output is a scalar, if `axis` is an integer, the rank of `output` is one less than the rank of `tensor`, if `axis` is a 2-tuple the rank of `output` is two less than the rank of `tensor`. |

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| ## Raises ||
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| `ValueError` | If `ord` or `axis` is invalid. |

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## numpy compatibility

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Mostly equivalent to numpy.linalg.norm.
Not supported: ord \<= 0, 2-norm for matrices, nuclear norm.
Other differences:
a) If axis is `None`, treats the flattened `tensor` as a vector
regardless of rank.
b) Explicitly supports 'euclidean' norm as the default, including for
higher order tensors.

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