# How to get the magnitude of a vector in NumPy?

The fundamental feature of linear algebra are vectors, these are the objects having both direction and magnitude. In Python, NumPy arrays can be used to depict a vector.

There are mainly two ways of getting the magnitude of vector:

• By defining an explicit function which computes the magnitude of a given vector based on the below mathematical formula:
```if V is vector such that, V = (a, b, c)
then ||V|| = ?(a*a + b*b + c*c)
```

Here are some programs which computes the magnitude of a vector following the above approach:

 `# program to compute magnitude of a vector ` ` `  `# importing required libraries ` `import` `numpy ` `import` `math ` ` `  `# function defination to compute magnitude o f the vector ` `def` `magnitude(vector):  ` `    ``return` `math.sqrt(``sum``(``pow``(element, ``2``) ``for` `element ``in` `vector)) ` ` `  `# displaying the original vector ` `v ``=` `numpy.array([``0``, ``1``, ``2``, ``3``, ``4``]) ` `print``(``'Vector:'``, v) ` ` `  `# computing and displaying the magnitude of the vector ` `print``(``'Magnitude of the Vector:'``, magnitude(v)) `

Output:

```Vector: [0 1 2 3 4]
Magnitude of the Vector: 5.477225575051661
```

Below is another example with the same approach:

 `# program to compute magnitude of a vector ` ` `  `# importing required libraries ` `import` `numpy ` `import` `math ` ` `  `# function defination to compute magnitude o f the vector ` `def` `magnitude(vector):  ` `    ``return` `math.sqrt(``sum``(``pow``(element, ``2``) ``for` `element ``in` `vector)) ` ` `  `# computing and displaying the magnitude of the vector ` `print``(``'Magnitude of the Vector:'``, magnitude(numpy.array([``1``, ``2``, ``3``]))) `

Output:

```Magnitude of the Vector: 3.7416573867739413
```
• By using the `norm()` method in `linalg` module of `NumPy` library. The Linear Algebra module of `NumPy` offers various methods to apply linear algebra on any `NumPy` array. Below are some programs which use `numpy.linalg.norm()` to compute the magnitude of a vector:

 `# program to compute magnitude of a vector ` ` `  `# importing required libraries ` `import` `numpy ` ` `  `# displaying the original vector ` `v ``=` `numpy.array([``1``, ``2``, ``3``]) ` `print``(``'Vector:'``, v) ` ` `  `# computing and displaying the magnitude of ` `# the vector using norm() method ` `print``(``'Magnitude of the Vector:'``, numpy.linalg.norm(v)) `

Output:

```Vector: [1 2 3]
Magnitude of the Vector: 3.7416573867739413
```

An additional argument `ord` can be used to compute the nth order of the `norm()` of a vector.

 `# program to compute the nth order of the  ` `# magnitude of a vector ` ` `  `# importing required libraries ` `import` `numpy ` ` `  `# displaying the original vector ` `v ``=` `numpy.array([``0``, ``1``, ``2``, ``3``, ``4``]) ` `print``(``'Vector:'``, v) ` ` `  `# computing and displaying the magnitude of the vector ` `print``(``'Magnitude of the Vector:'``, numpy.linalg.norm(v)) ` ` `  `# Computing the nth order of the magnitude of vector ` `print``(``'ord is 0: '``, numpy.linalg.norm(v, ``ord` `=` `0``)) ` `print``(``'ord is 1: '``, numpy.linalg.norm(v, ``ord` `=` `1``)) ` `print``(``'ord is 2: '``, numpy.linalg.norm(v, ``ord` `=` `2``)) ` `print``(``'ord is 3: '``, numpy.linalg.norm(v, ``ord` `=` `3``)) ` `print``(``'ord is 4: '``, numpy.linalg.norm(v, ``ord` `=` `4``)) `

Output:

```Vector: [0 1 2 3 4]
Magnitude of the Vector: 5.477225575051661
ord is 0:  4.0
ord is 1:  10.0
ord is 2:  5.477225575051661
ord is 3:  4.641588833612778
ord is 4:  4.337613136533361
```

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