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

Access provided by NIH/NIMH

11,587 already enrolled

5 modules

Gain insight into a topic and learn the fundamentals.

189 reviews

Intermediate level

Recommended experience

8 hours to complete

Flexible schedule

Learn at your own pace

5 modules

Gain insight into a topic and learn the fundamentals.

189 reviews

Intermediate level

Recommended experience

8 hours to complete

Flexible schedule

Learn at your own pace

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

Details to know

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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

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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 videos1 reading2 assignments

13 videos Total 74 minutes

Introduction to the Course 1 minute
Linear System and Definition 3 minutes
Three Solution Options and Coordinate System Visualization 4 minutes
Linear System -> Matrix (Coefficient and Augmented) 5 minutes
Rules of G.E. and Solving a Linear System 4 minutes
G.E. Intuition and Simple Example 5 minutes
G.E Example - Single Solution Part 1 12 minutes
G.E Example - Single Solution Part 2 7 minutes
G.E Example - Single Solution Part 3 + Meaning 3 minutes
G.E. Example - Infinite Solutions 4 minutes
G.E. Example - No Solutions 8 minutes
G.E. Advanced Example - Part 1 8 minutes
G.E. Advanced Example - Part 2 11 minutes

1 reading Total 1 minute

Course Updates and Accessibility Support 1 minute

2 assignments Total 15 minutes

Practice - Linear System -> Matrix Format 5 minutes
LS -> Matrix + G.E. Full Question Quiz 10 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 videos Total 35 minutes

Matrix Algebra Sum 5 minutes
Matrix Algebra Scale + Identity Overview 4 minutes
Matrix Multiplication + Small Example 9 minutes
Matrix Multiplication - General Rules 5 minutes
Matrix Multiplication Example 6 minutes
Identity Matrix + Example 7 minutes

2 assignments Total 30 minutes

Quiz on Matrix Algebra Sum + Scale 15 minutes
Matrix Multiplication 15 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 videos Total 87 minutes

Introduction to Vectors + Coordinates 7 minutes
Introduction to Linear Combinations 3 minutes
Linear Combinations 2 minutes
Linear Combinations Example 10 minutes
Span 5 minutes
Span Example 10 minutes
Ax = b 8 minutes
Linear Independence 5 minutes
Linear Independence Example Part 1 8 minutes
Linear Independence Example Part 2 4 minutes
Columns of a Matrix Being Linearly Independent 5 minutes
Linear Transformations 3 minutes
Linear Transformations Example 4 minutes
Matrix Inverse 4 minutes
Matrix Inverse Example 8 minutes

3 assignments Total 35 minutes

Why do we use matrices and vectors and not just one? 5 minutes
Quiz on Linear Independence 10 minutes
Quiz on Transformations and Inverse 20 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.

What's included

8 videos3 assignments

8 videos Total 51 minutes

Determinant Intro and 2x2 Example 2 minutes
Inverse of 2x2 Matrix - Quick Method 5 minutes
Determinant of 3x3 Matrix - Overview 8 minutes
Determinant of 3x3 Matrix - Example with 1st Row 7 minutes
Determinant of 3x3 Matrix - Example with 2nd Row 8 minutes
Eigenvalue and Eigenvector - Overview 6 minutes
Finding Eigenvector if Given Eigenvalue 9 minutes
Characteristic Polynomic - Finding Eigenvalues 7 minutes

3 assignments Total 30 minutes

Find the Determinant of a 2x2 Matrix 5 minutes
Find Eigenvalue then Eigenvector of a Matrix (2x2) 10 minutes
Find Eigenvalue then Eigenvector of a Matrix (3x3) 15 minutes

In this module we will learn how to compute the determinant of a matrix. Afterwards, Eigenvalues and Eigenvectors will be covered.

What's included

9 videos3 assignments

9 videos Total 41 minutes

Transpose and Inner (Dot) Product 7 minutes
Norm (Length) of a Vector 4 minutes
Unit Vector Creation 4 minutes
Distance Between Two Vectors 3 minutes
Orthogonal Vectors 4 minutes
Orthogonal Projections Part I 5 minutes
Orthogonal Projections Part II 2 minutes
Least Squares Overview 5 minutes
Least Squares Example 7 minutes

3 assignments Total 70 minutes

Important Final Concepts 30 minutes
Finding Least Squares Solutions 10 minutes
Final Exam 30 minutes

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