Gain insights into linear algebra essentials for data science, focusing on vectors, matrices, and tensors. Explore practical Python applications, engaging visuals, real datasets, and hands-on projects.

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Linear algebra is a fundamental pillar of data science. In advanced models in data science, like neural networks, the inputs and transformations are based upon vectors, matrices, and tensors which require a reasonable understanding of linear algebra to get the desired results. It is elegant and the most applied mathematics under the umbrella of data science.

This course teaches linear algebra with a focus on data science. This course encompasses several engaging illustrations, including static images and animations. Furthermore, this course presents mathematical modeling through programming in Python. This course contains several executable coding playgrounds on real data sets and a final project with practical applications.

Aside from theoretical implementations, the modern-day world needs its daunting calculations, trajectory mapping, and distance manipulation, all of which linear algebra provides. By the end of this course, you’ll have a working knowledge of all the necessary teachings in linear algebra.

Linear Algebra for Data Science Using Python

# From abstract to real vector space
All data (text, images, videos, sound) is made up of data points or samples, which can be represented as column vectors having $d$ real numbers. That said, we already know that all d-dimensional vectors compose the $\R^d$  vector space over the field $\R$. So, we can say that $\R^d$ is the most popular vector space used in data science because all data is represented using vectors that span $\R^d$. Here, $d$ represents the dimension of the vector space, $\R^d$.

## Image is a point in space
Consider a $4 \times 4$ matrix of intensities of a grayscale image shown in the figure below. Each intensity value can be considered a feature of the image, so we can say that it has a total of 16 features. We can represent these features as a column vector in $\R^{16}$ by *flattening* the image, say, row-wise. Even if we don't flatten the image, it's still a vector/point in the space of $4 \times 4$ matrices denoted by $M^{4 \times 4}$. 

Learn how vector spaces are relevant in data science.

Introduction

Linearity

Matrices

Solving Linear Systems

Singularity

Linear Regression and Least Squares

Vector Space

Vector Spaces of a Matrix

Singular Value Decomposition: SVD

Learning to Find Discriminative Null Space for Face Recognition

Vector Space in Data Science

From abstract to real vector space