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Linear Algebra for Data Science Using Python

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.

Beginner

67 Lessons

10h

Certificate of Completion

AI-POWERED

Explanations

AI-POWERED

Explanations

This course includes

1 Project

170 Playgrounds

8 Challenges

9 Quizzes

Course Overview

What You'll Learn

Course Content

Course Overview

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 a...Show More

What You'll Learn

Learning the intricate concepts of linear algebra from scratch

Working knowledge of various linear algebra techniques using Python

A visual understanding of concepts such as vector space, spans, and subspace with animations

Familiarity with valuable concepts like fields, eigenspaces, diagonalization, and SVD

An understanding of how linear algebra concepts build the most useful tools in data science, such as neural networks

The ability to apply linear algebra concepts to real-world problems through coding exercises and practical projects

Learning the intricate concepts of linear algebra from scratch

Course Content

Introduction

1 Lessons

Get familiar with linear algebra applications in data science using Python.

Course Objectives

Linearity

11 Lessons

Get started with linear functions, linear combinations, and solving linear systems in data science.

Functions

Functions in Data Science

Linear Functions

Linear Combinations

Quiz: Linear Functions and Combinations

Challenge: Linear Combination Checker

Convex Combinations

Linear Independence

Linear Systems

Quiz: Convex Combinations and Linear Independence

Challenge: Linear System Solver

Matrices

5 Lessons

Master the steps to utilize matrices and perform matrix operations essential for data science.

Matrices

Matrix Multiplication

Matrix Operations

Quiz: Matrices and Matrix Operations

Challenge: Matrix Multiplier

Solving Linear Systems

12 Lessons

Grasp the fundamentals of solving linear systems, Gaussian elimination, and matrix rank.

Solution Preserving Operations

Echelon Matrices

Gaussian Elimination

Gaussian Elimination Using Python

Solution Set of a Linear System

Geometric Interpretation of Inconsistency

Verifying Linear Independence

Rank of a Matrix

Challenge: Check Linear Independence

Solution Set and Rank

Quiz: Linear Systems

Challenge: Calculate the Largest Independent Subset

Singularity

7 Lessons

Map out the steps for working with matrices in data science using elementary transformations.

Elementary Matrices

Inverse of a Square Matrix

Determinant of a Matrix

Determinant by Pivots: A Python Algorithm

Inverse of a Rectangular Matrix

Quiz: Elementary and Invertible Matrix

Challenge: Lower-upper Decomposition Algorithm

Linear Regression and Least Squares

11 Lessons

Focus on linear and non-linear regression techniques, practical applications, multi-target regression, and neural networks.

Approximate Solution

Least Squared Error Solution

Challenge: Sum of Squared Error Calculator

Linear Regression

Linear Regression on Real Dataset

Multi-target Linear Regression

Polynomial Regression

Non-linear Regression

Classification Through Regression

Neural Networks

Quiz: Regression and Classification

Vector Space

12 Lessons

Build on vector properties, sets, fields, vector spaces, subspaces, and applications in data science.

Vector Generalization

Set and Closure Property

Span, Basis, and Dimensions

Subspace

Dot Product vs. Inner Product

Vector Space in Data Science

Quiz: Vector Space, Span, and Basis

Challenge: Subspace Dimension Finder

Vector Spaces of a Matrix

5 Lessons

Step through vector spaces, null spaces, orthogonal complements, and eigenspaces in matrix algebra.

Column Space

Row Space and Null Space

Orthogonal Spaces and Complements

Eigenspace

Quiz: Null Space and Orthogonal Space

Singular Value Decomposition: SVD

3 Lessons

Get started with orthogonal diagonalization and Singular Value Decomposition (SVD) for matrix factorization.

Orthogonal Diagonalization

Singular Value Decomposition: SVD

Quiz: Diagonalization and SVD

Learning to Find Discriminative Null Space for Face Recognition

Project

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