- CONTENTS
- First, what is a Vector?
- Creation of a Vector in Python
- Basic Operations on a Python Vector
- 1. Performing addition operation on a Python Vector
- 2. Performing Subtraction of two vectors
- 3. Performing multiplication of two vectors
- 4. Performing Vector division operation
- 5. Vector Dot Product
- Conclusion

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Hello, folks! Today, we will be having a look at one of the most unaddressed topics in Python that is, **Vectors** in Python. So, let us begin!

**A vector** in a simple term can be considered as a single-dimensional array. With respect to Python, a vector is a **one-dimensional array** of lists. It occupies the elements in a similar manner as that of a Python list.

Let us now understand the Creation of a vector in Python.

Python NumPy module is used to create a vector. We use `numpy.array()`

method to create a one-dimensional array i.e. a vector.

**Syntax:**

```
numpy.array(list)
```

**Example 1:** Horizontal Vector

```
import numpy as np
lst = [10,20,30,40,50]
vctr = np.array(lst)
vctr = np.array(lst)
print("Vector created from a list:")
print(vctr)
```

**Output:**

```
Vector created from a list:
[10 20 30 40 50]
```

**Example 2:** Vertical Vector

```
import numpy as np
lst = [[2],
[4],
[6],
[10]]
vctr = np.array(lst)
vctr = np.array(lst)
print("Vector created from a list:")
print(vctr)
```

**Output:**

```
Vector created from a list:
[[ 2]
[ 4]
[ 6]
[10]]
```

Having created a Vector, now let us perform some basic operations on these Vectors now!

Here is a list of the basic operations that can be performed on a Vector–

**Addition****Subtraction****Multiplication****Division****Dot Product**, etc.

Let us begin!

Below, we have performed **Vector addition** operation on the vectors.

The addition operation would take place in an `element-wise manner`

i.e. element by element and further the resultant vector would have the same length as of the two additive vectors.

**Syntax:**

```
vector + vector
```

**Example:**

```
import numpy as np
lst1 = [10,20,30,40,50]
lst2 = [1,2,3,4,5]
vctr1 = np.array(lst1)
vctr2= np.array(lst2)
print("Vector created from a list 1:")
print(vctr1)
print("Vector created from a list 2:")
print(vctr2)
vctr_add = vctr1+vctr2
print("Addition of two vectors: ",vctr_add)
```

**Output:**

```
Vector created from a list 1:
[10 20 30 40 50]
Vector created from a list 2:
[1 2 3 4 5]
Addition of two vectors: [11 22 33 44 55]
```

On similar lines, in **subtraction** as well, the element-wise fashion would be followed and further the elements of vector 2 will get subtracted from vector 1.

Let us have a look at it’s implementation!

```
import numpy as np
lst1 = [10,20,30,40,50]
lst2 = [1,2,3,4,5]
vctr1 = np.array(lst1)
vctr2= np.array(lst2)
print("Vector created from a list 1:")
print(vctr1)
print("Vector created from a list 2:")
print(vctr2)
vctr_sub = vctr1-vctr2
print("Subtraction of two vectors: ",vctr_sub)
```

**Output:**

```
Vector created from a list 1:
[10 20 30 40 50]
Vector created from a list 2:
[1 2 3 4 5]
Subtraction of two vectors: [ 9 18 27 36 45]
```

In a **Vector multiplication**, the elements of vector 1 get multiplied by the elements of vector 2 and the product vector is of the same length as of the multiplying vectors.

Let us try to visualize the multiplication operation:

x = [10,20] and y = [1,2] are two vectors. So the product vector would be v[ ],

**v[0] = x[0] * y[0]
v[1] = x[1] * y[1]**

Have a look at the below code!

```
import numpy as np
lst1 = [10,20,30,40,50]
lst2 = [1,2,3,4,5]
vctr1 = np.array(lst1)
vctr2= np.array(lst2)
print("Vector created from a list 1:")
print(vctr1)
print("Vector created from a list 2:")
print(vctr2)
vctr_mul = vctr1*vctr2
print("Multiplication of two vectors: ",vctr_mul)
```

**Output:**

```
Vector created from a list 1:
[10 20 30 40 50]
Vector created from a list 2:
[1 2 3 4 5]
Multiplication of two vectors: [ 10 40 90 160 250]
```

In **vector division**, the resultant vector is the quotient values after carrying out division operation on the two vectors.

Consider the below example for a better understanding.

x = [10,20] and y = [1,2] are two vectors. So the resultant vector v would be,

**v[0] = x[0] / y[0]
v[1] = x[1] / y[1]**

Let us now implement the above concept.

**Example**:

```
import numpy as np
lst1 = [10,20,30,40,50]
lst2 = [10,20,30,40,50]
vctr1 = np.array(lst1)
vctr2= np.array(lst2)
print("Vector created from a list 1:")
print(vctr1)
print("Vector created from a list 2:")
print(vctr2)
vctr_div = vctr1/vctr2
print("Division of two vectors: ",vctr_div)
```

**Output:**

```
Vector created from a list 1:
[10 20 30 40 50]
Vector created from a list 2:
[10 20 30 40 50]
Multiplication of two vectors: [ 1 1 1 1 1 ]
```

In a **vector dot product**, we perform the summation of the product of the two vectors in an element-wise fashion.

Let us have a look at the below.

**vector c = x . y = (x1 * y1 + x2 * y2)**

**Example:**

```
import numpy as np
lst1 = [10,20,30,40,50]
lst2 = [1,1,1,1,1]
vctr1 = np.array(lst1)
vctr2= np.array(lst2)
print("Vector created from a list 1:")
print(vctr1)
print("Vector created from a list 2:")
print(vctr2)
vctr_dot = vctr1.dot(vctr2)
print("Dot product of two vectors: ",vctr_dot)
```

**Output:**

```
Vector created from a list 1:
[10 20 30 40 50]
Vector created from a list 2:
[1 1 1 1 1]
Dot product of two vectors: 150
```

By this, we have come to the end of this topic.

In order to have a deeper understanding about vectors, do try out creating a vector and performing the above mentioned operations and let us know your understanding in the comment box!

Feel free to comment below, in case you come across any question. For more such posts related to Python, Stay tuned and till then,

Happy Learning!! :)

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In examples 1 and 2, why do you create vctr twice?

- Ged Toon

Hi, would be interesting also the case of vector cross product There seems to be also numpy.cross I tried just it and found it doesn’t work with syntax similar to dot product. This will cause error: >>> alst = [4, 1] >>> blst = [-1, 4] >>> avctr = np.array(alst) >>> bvctr = np.array(blst) >>> avctr.cross(bvctr) Traceback (most recent call last): File “”, line 1, in AttributeError: ‘numpy.ndarray’ object has no attribute ‘cross’ However, this works giving only the sum of the squares, i.e the squares of the vector lengths: >>> cvtr = np.cross(avctr, bvctr) >>> cvtr array(17) Changing order of the vectors: >>> cvtr = np.cross(bvctr, avctr) >>> cvtr array(-17) One thing is still missing! How do you get the resulting vector, a 3D array[i, j, k]? It should be in this example the vectors [0, 0, 17] or [0, 0, -17], perpendicular to the vectors avctr and bvctr.

- Jarmo Lammi

You have errors at 4. Performing Vector division operation There was mixed operator / and * The following example would have more sense. >>> lst1 = [10, 20, 30, 40, 50] >>> lst2 = [1, 2, 3, 4, 5] >>> vctr1 = np.array(lst1) >>> vctr2 = np.array(lst2) >>> vctr_div1 = vctr1/vctr2 >>> vctr_div1 array([10., 10., 10., 10., 10.]) >>> vctr_div2 = vctr2/vctr1 >>> vctr_div2 array([0.1, 0.1, 0.1, 0.1, 0.1]) >>> vctr_mul_div = vctr_div1*vctr_div2 >>> vctr_mul_div array([1., 1., 1., 1., 1.])

- Jarmo Lammi