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.

linearalgebra.tar.gz

Code

visualizing-planes-3D

line-graph

convex-combinations-animation

intersecting planes

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

Given a system of linear equations, there are two questions we can ask about its solution:
* Does a solution exist?
* If a solution exists, is it unique?


## Solution set of a linear system and $rref$
Because the reduced row echelon form ($rref$) is the maximally simplified version of a linear system, it's easier to comprehend the solution from the $rref$ than from the original system. The two questions stated above can be answered by a simple analysis of $rref$ of a linear system. However, to perform that analysis, we need to be familiar with a few simple terminologies.

### Pivot variables vs. free variables
A variable with a corresponding column that has a pivot is called a **pivot variable**. In contrast, a variable with a corresponding column in $rref$ that doesn’t contain a pivot is called a **free variable**.

Given a system of linear equations, there are two questions we can ask about its solution:
* Does a solution exist?
* If a solution exists, is it unique?


# Solution set of a linear system and $rref$
Because the reduced row echelon form ($rref$) is the maximally simplified version of a linear system, it's easier to comprehend the solution from the $rref$ than from the original system. The two questions stated above can be answered by a simple analysis of $rref$ of a linear system. However, to perform that analysis, we need to be familiar with a few simple terminologies.

## Pivot variables vs. free variables
A variable with a corresponding column that has a pivot is called a **pivot variable**. In contrast, a variable with a corresponding column in $rref$ that doesn’t contain a pivot is called a **free variable**.

Learn about the different possible solutions of a linear system and how to interpret them using reduced row echelon form.

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

Solution Set of a Linear System