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

An elementary matrix is a square matrix that represents an elementary row operation. These matrices help us automate matrix transformations and decompositions.

## Creation of an elementary matrix

To create an elementary matrix, $E_{n \times n}$, we start with the identity matrix, $I_{n\times n}$, and apply the desired elementary row operation to it. The resultant matrix is the elementary matrix corresponding to the given operation.

### Row swap
An elementary matrix for row swap is an identity matrix with the two rows interchanged. These matrices are also called permutation matrices, represented by $P_{ij}$, where $i$ and $j$ represent the two rows to be swapped. For example, the elementary matrix to swap the second and third rows is as follows:

$$P_{23}=\begin{bmatrix}
1 & 0 & 0\\
0 & 0 & 1\\
0 & 1 & 0
\end{bmatrix}$$




An elementary matrix is a square matrix that represents an elementary row operation. These matrices help us automate matrix transformations and decompositions.

# Creation of an elementary matrix

To create an elementary matrix, $E_{n \times n}$, we start with the identity matrix, $I_{n\times n}$, and apply the desired elementary row operation to it. The resultant matrix is the elementary matrix corresponding to the given operation.

## Row swap
An elementary matrix for row swap is an identity matrix with the two rows interchanged. These matrices are also called permutation matrices, represented by $P_{ij}$, where $i$ and $j$ represent the two rows to be swapped. For example, the elementary matrix to swap the second and third rows is as follows:

$$P_{23}=\begin{bmatrix}
1 & 0 & 0\\
0 & 0 & 1\\
0 & 1 & 0
\end{bmatrix}$$




Learn about elementary and  elimination matrices. 

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

Elementary Matrices

Creation of an elementary matrix

Row swap