Basic concepts of linear algebra

I will be showing all examples in Python using the NumPy library.

First of all, we must import the library:

import numpy as np

Concepts

Theory might seem boring, but it is necessary to build the foundation we need to correctly handle practical topics.

What is a scalar?

These are quantities that only have magnitude. Simply put, it's just a number.

What is a vector?

It is an ordered list of scalars that describe an object.

Why ordered? Because the vector [2, 5] is not the same as [5, 2].

For example, we could represent the ratings a movie has in different genres:

# Action, Drama, Comedy
movie = np.array([2.4, 5.8, 8.7])

What is a matrix?

It is a two-dimensional set of numbers in a rectangular shape, organized in rows and columns.

In Machine Learning, rows represent observations and columns represent features.

movies = np.array([
    [8.5, 4.0, 6.5, 7.5],  # Movie A
    [5.0, 9.0, 6.0, 8.0],  # Movie B
    [9.0, 2.0, 7.0, 6.5]   # Movie C
])

What is a tensor?

These are mathematical objects that store numerical values and can have various dimensions.

More information: https://telefonicatech.com/blog/deep-learning-para-todos-los-publicos

For example, we can represent a pixel on our screen. First, you have to understand that a pixel is made up of three color values, where each one represents a channel (RGB).

image = np.array([
    [
        [255, 0, 0], # Red,
        [0, 255, 0], # Green
        [0, 0, 255] # Blue
    ],
])

# Graph
plt.imshow(image)
plt.title("Tensor Image")
plt.axis('off')
plt.show()

Example of Tensor pixel

Summary

The foundations of today's world rely heavily on linear algebra, especially in Artificial Intelligence.
NumPy and Matplotlib are fundamental tools that you must know how to use.
A scalar is a number.
A vector is an ordered list of scalars representing an object.
A matrix is a table of numbers, where rows are observations and columns are features.
A tensor is a mathematical object that stores numerical values and can have different dimensions (1D, 2D, 3D, 4D, etc.).

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