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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

11,860 already enrolled

Included with

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5 modules

Gain insight into a topic and learn the fundamentals.

190 reviews

Intermediate level

Recommended experience

Flexible schedule

8 hours to complete

Learn at your own pace

Prepare for a degree

Learn more

5 modules

Gain insight into a topic and learn the fundamentals.

190 reviews

Intermediate level

Recommended experience

Flexible schedule

8 hours to complete

Learn at your own pace

Prepare for a degree

Learn more

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

Shareable certificate

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Assessments

13 assignments

Taught in English

91% of learners achieved a positive career outcome

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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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Gain a foundational understanding of a subject or tool
Develop job-relevant skills with hands-on projects
Earn a shareable career certificate

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.

Module details

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 videosTotal 74 minutes

Introduction to the Course1 minute
Linear System and Definition3 minutes
Three Solution Options and Coordinate System Visualization4 minutes
Linear System -> Matrix (Coefficient and Augmented)5 minutes
Rules of G.E. and Solving a Linear System4 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 Solutions4 minutes
G.E. Example - No Solutions8 minutes
G.E. Advanced Example - Part 18 minutes
G.E. Advanced Example - Part 211 minutes

1 readingTotal 1 minute

Course Updates and Accessibility Support1 minute

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

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 minutes
Introduction to Linear Combinations3 minutes
Linear Combinations2 minutes
Linear Combinations Example10 minutes
Span5 minutes
Span Example10 minutes
Ax = b8 minutes
Linear Independence5 minutes
Linear Independence Example Part 18 minutes
Linear Independence Example Part 24 minutes
Columns of a Matrix Being Linearly Independent5 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.

What's included

8 videos3 assignments

8 videosTotal 51 minutes

Determinant Intro and 2x2 Example2 minutes
Inverse of 2x2 Matrix - Quick Method5 minutes
Determinant of 3x3 Matrix - Overview8 minutes
Determinant of 3x3 Matrix - Example with 1st Row7 minutes
Determinant of 3x3 Matrix - Example with 2nd Row8 minutes
Eigenvalue and Eigenvector - Overview6 minutes
Finding Eigenvector if Given Eigenvalue9 minutes
Characteristic Polynomic - Finding Eigenvalues7 minutes

3 assignmentsTotal 30 minutes

Find the Determinant of a 2x2 Matrix5 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 videosTotal 41 minutes

Transpose and Inner (Dot) Product7 minutes
Norm (Length) of a Vector4 minutes
Unit Vector Creation4 minutes
Distance Between Two Vectors3 minutes
Orthogonal Vectors4 minutes
Orthogonal Projections Part I5 minutes
Orthogonal Projections Part II2 minutes
Least Squares Overview5 minutes
Least Squares Example7 minutes

3 assignmentsTotal 70 minutes

Important Final Concepts30 minutes
Finding Least Squares Solutions10 minutes
Final Exam30 minutes

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Taking this course by University of Colorado Boulder may provide you with a preview of the topics, materials and instructors in a related degree program which can help you decide if the topic or university is right for you.