# Vector Operation - ( Tensors in PyTorch )

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### Syntax

#### Vector Addition

```
import torch
a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
c = a + b
print(c)
```

#### Scalar Multiplication

```
import torch
a = torch.tensor([1, 2, 3])
b = 2
c = a * b
print(c)
```

#### Dot Product

```
import torch
a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
c = torch.dot(a, b)
print(c)
```

### Example

#### Vector Addition

```
import torch
a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
c = a + b
print(c)
```

Output:

```
tensor([5, 7, 9])
```

#### Scalar Multiplication

```
import torch
a = torch.tensor([1, 2, 3])
b = 2
c = a * b
print(c)
```

Output:

```
tensor([2, 4, 6])
```

#### Dot Product

```
import torch
a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
c = torch.dot(a, b)
print(c)
```

Output:

```
tensor(32)
```

### Explanation

Vector operations are fundamental to machine learning tasks, as data is often represented in the form of vectors. Some of the key vector operations are vector addition, scalar multiplication, and dot product.

Vector addition involves adding vectors element-wise. Scalar multiplication involves multiplying a vector by a scalar, which scales the vector. The dot product involves multiplying the corresponding elements of two vectors, and adding the results.

In PyTorch, vectors are represented using tensors, which are similar to arrays in other programming languages. Tensors in PyTorch are efficient for numerical computations in machine learning.

### Use

Vector operations are used in machine learning for various tasks, such as data processing, feature extraction, and model training. Vector addition can be used, for example, to combine features from different sources. Scalar multiplication can be used to scale and normalize features. Dot product can be used to compute similarity between vectors, which is used in various machine learning tasks such as recommendation systems and search engines.

### Important Points

- Vector operations are fundamental to machine learning tasks
- Vector addition, scalar multiplication and dot product are key vector operations
- In PyTorch, vectors are represented using tensors
- Tensors are efficient for numerical computations in machine learning

### Summary

In summary, vector operations are essential for machine learning tasks, and PyTorch provides efficient support for manipulating vectors through its tensor data structure. Vector addition, scalar multiplication and dot product are fundamental vector operations, and are used in many different machine learning applications, such as data processing, feature extraction, and model training.