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

# Set
A **set** is a collection of objects fulfilling the following two properties:

*  **Unordered:** There’s no particular order of the objects in a set. It doesn’t matter if an object is the first or seventh.
* **Distinct**: All objects in the set are distinct.






# Set notation
A set is mathematically represented by curly braces $\{\ \}$ and is typically denoted by a capital letter. In the case that mentioning all the elements isn’t feasible, we resort to the set builder notation. The **set builder notation** allows us to represent a set in a concise manner.

# Examples of sets
|  Description | Mathematical Representation  |
| :- | :- |
| Set of natural numbers not exceeding 10 | $A = \{1,2,3,4,5,6,7,8,9,10\} \hspace{16mm}$ $A = \{x$ &#124; $x \in N \wedge 1 \le x \le 10\}$ |
|Set of $2 \times 2$ symmetric matrices| $M = \bigg\{ \begin{bmatrix} a&b\\b&c \end{bmatrix}$ &#124; $a,b,c \in \R  \bigg\}$ |
| Set of linear equations in $n$ unknowns  | $L = \{w_1x_1+\cdots + w_nx_n=b$ &#124; $x_i,w_i,b\in \R\}$ |


Learn the definition of set, its mathematical representation, and closure property with examples.

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

Set and Closure Property

Set

Set notation

Examples of sets

Description	Mathematical Representation
Set of natural numbers not exceeding 10	$A = \{1,2,3,4,5,6,7,8,9,10\} \hspace{16mm}$ $A = \{x$ \| $x \in N \wedge 1 \le x \le 10\}$
Set of $2 \times 2$ symmetric matrices	$M = \bigg\{ \begin{bmatrix} a&b\\b&c \end{bmatrix}$ \| $a,b,c \in \R \bigg\}$
Set of linear equations in $n$ unknowns	$L = \{w_1x_1+\cdots + w_nx_n=b$