Essential Linear Algebra for Data Science

Essential Linear Algebra for Data Science

This course is part of Expressway to Data Science: Essential Math Specialization

Instructor: James Bird

What you'll learn

Solve real-world problems using the foundational concept of matrices and explain where those problems might arise.
Recognize what a matrix represents in n-dimensional space and how transformations act in that space
Identify key properties of any system of equations, such as independence, basis, rank, and more, and what they mean for the overall system.
Demonstrate your understanding of projections in lower dimensions, while being able to carry out higher dimension projections for real-world problems

Skills you'll gain

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Assessments

13 assignments

Taught in English

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This course is part of the Expressway to Data Science: Essential Math Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 5 modules in this course

Are you interested in Data Science but lack the math background for it? Has math always been a tough subject that you tend to avoid? This course will teach you the most fundamental Linear Algebra that you will need for a career in Data Science without a ton of unnecessary proofs and concepts that you may never use. Consider this an expressway to Data Science with approachable methods and friendly concepts that will guide you to truly understanding the most important ideas in Linear Algebra.

In this module we will learn what a matrix is and what it represents. We will explore how a system of linear equations can be expressed in a neat package via matrices. Lastly, we will delve into coordinate systems and provide visualizations to help you understand matrices in a more well-rounded way.

What's included

13 videos2 assignments

13 videosTotal 74 minutes

Introduction to the Course1 minutePreview module
Linear System and Definition3 minutes
Three Solution Options and Coordinate System Visualization3 minutes
Linear System -> Matrix (Coefficient and Augmented)4 minutes
Rules of G.E. and Solving a Linear System3 minutes
G.E. Intuition and Simple Example5 minutes
G.E Example - Single Solution Part 112 minutes
G.E Example - Single Solution Part 27 minutes
G.E Example - Single Solution Part 3 + Meaning3 minutes
G.E. Example - Infinite Solutions3 minutes
G.E. Example - No Solutions7 minutes
G.E. Advanced Example - Part 17 minutes
G.E. Advanced Example - Part 210 minutes

2 assignmentsTotal 15 minutes

Practice - Linear System -> Matrix Format5 minutes
LS -> Matrix + G.E. Full Question Quiz10 minutes

In this module we will learn how to solve a linear system of equations with matrix algebra.

What's included

6 videos2 assignments

6 videosTotal 34 minutes

Matrix Algebra Sum4 minutesPreview module
Matrix Algebra Scale + Identity Overview3 minutes
Matrix Multiplication + Small Example8 minutes
Matrix Multiplication - General Rules4 minutes
Matrix Multiplication Example6 minutes
Identity Matrix + Example6 minutes

2 assignmentsTotal 30 minutes

Quiz on Matrix Algebra Sum + Scale15 minutes
Matrix Multiplication15 minutes

In this module we will explore concepts and properties of linear systems. This includes independence, basis, rank, row space, column space, and much more.

What's included

15 videos3 assignments

15 videosTotal 87 minutes

Introduction to Vectors + Coordinates7 minutesPreview module
Introduction to Linear Combinations2 minutes
Linear Combinations2 minutes
Linear Combinations Example10 minutes
Span5 minutes
Span Example9 minutes
Ax = b8 minutes
Linear Independence4 minutes
Linear Independence Example Part 18 minutes
Linear Independence Example Part 24 minutes
Columns of a Matrix Being Linearly Independent4 minutes
Linear Transformations3 minutes
Linear Transformations Example4 minutes
Matrix Inverse4 minutes
Matrix Inverse Example8 minutes

3 assignmentsTotal 35 minutes

Why do we use matrices and vectors and not just one?5 minutes
Quiz on Linear Independence10 minutes
Quiz on Transformations and Inverse20 minutes

In this module we will discuss projections and how they work. We will build on a foundation using 2-dimensional projections and explore the concept in higher dimensions over time.