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

# Rank
The **rank** of a matrix $A$, denoted by $r(A)$, is defined as the number of linearly independent rows of $A$.

By definition, a coefficient matrix, $A$, represents a linearly independent system of $r(A)$ equations. The number of linearly independent rows is called **row rank**, and the number of linearly independent columns is called **column rank**. However, because row rank is always equal to column rank, these terms are seldom used. Instead, we simply refer to them as rank.



## Calculating rank through Python
The following Python code calculates the rank of a matrix.


import numpy as np

mat = np.array([[2, 3, -4, 7],
                [1, 6, -5, 1],
                [-2, 1, 10, -4]])
print(mat)
rank = np.linalg.matrix_rank(mat)    
print("The rank of the matrix is", rank)

## Rank and $rref$
The rank of a matrix, $A$, equals the number of pivots in the $rref$ of $A$."

This follows from our previous discussion on linearly dependent rows in $rref$. All linearly dependent rows are converted into _all-zero rows_ in $rref$, and we’re left with only the linearly independent rows as the nonzero rows. Each nonzero row in $rref$ has a pivot. We can say that:
 $$r(A) = \text{number of pivots in }rref$$
The following code computes the rank of a matrix by counting the number of pivots in $rref$.



Learn about the rank of a matrix and its properties.

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

Rank of a Matrix

Rank

Calculating rank through Python

Rank and $rref$

Learning to Find Discriminative Null Space for Face Recognition

Rank of a Matrix

Rank

Calculating rank through Python

Rank and rrefrrefrref

Rank and $rref$