Master Linear Algebra 2020: The Complete Study Of Spaces
4.3 (360 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
5,912 students enrolled

Master Linear Algebra 2020: The Complete Study Of Spaces

Learn How to Define Space And How it is Characterized And Measured. We Make Linear Algebra Math Fun And Easy.
4.3 (360 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
5,912 students enrolled
Created by Kody Amour
Last updated 10/2017
English [Auto]
Current price: $13.99 Original price: $19.99 Discount: 30% off
5 hours left at this price!
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This course includes
  • 5.5 hours on-demand video
  • 36 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Solve linear systems
  • Understand matrix algebra
  • Know how to find the determinant of any matrix
  • Understand vector spaces and their properties
  • Understand what a basis is and how to apply it
  • Understand linear transformations
  • Understand eigenvectors
  • Understand norms
  • Understand inner products
  • Algebra from high school
  • For inner products sections, we will give examples involving integrals...

Have you ever wanted to fully understand the fourth dimension? How about the fifth? How about a space that is infinite dimensional? This is likely the most applicable mathematics course ever. We cover in depth everything about dots, lines, planes, spaces, and whatever is beyond that. We detail special functions on them and redefine everything that you have ever learned. Prepare to have your mind blown!

Master and Learn Everything Involving Spaces

  • Vector Spaces
  • Linear Transformations
  • How to Measure Space
  • Definition of a Right Angle (The Real One)
  • Inner-Product Spaces
  • Eigenvalues and Eigenvectors

Linear Algebra Can Be Easy. Start Your Course Today!

This course includes everything that a university level linear algebra course has to offer *guaranteed*. This course is great to take before or during your linear algebra course. The book isn't enough - trust me. You will succeed with these lectures. It's hard to believe that such a difficult class can be made simple and fun, but I promise that it will be. This is a topic that is widely used with everyone, and can be understood. The reason that I succeeded in my linear algebra course is because I had a great professor, and you deserve one too! So what are you waiting for?

Join today!

Who this course is for:
  • Potential Engineers
  • Potential Mathematicians
  • Those interested in Algebra
Course content
Expand all 70 lectures 11:31:18
+ Introduction
2 lectures 15:08

Welcome to the course! I'm so glad to have you as a student and I want to give you resources that you can use throughout this course.


The great thing about this course is that you only need to know some algebra from high school. If you forgot it, we will teach it from scratch again.

Brief Review of Algebra and Notation
+ Matrices and Their Properties
27 lectures 01:53:40

Here we show that the elimination method is really the fastest way to tackle systems of linear equations.

Solving Systems of Linear Equations
System of Equations Reading
14 pages
Solving Systems of Equations Reading
20 pages

This lecture, we define RREF and show how to tackle systems of linear equations.

Reduced Row Echelon Form Part 1

In this lecture, we solidify our understanding of RREF and go through a nice example.

Reduced Row Echelon Form Part 2

Some RREF problems aren't very nice and some systems tell us little information. In this lecture, we see how to get that little information.

RREF Example

This course is all about matrices. Here, we see some of the key operations we use with them.

Matrix Algebra Part 1
Matrix Arithmetic and Operations Reading
13 pages

In this lecture, we introduce how matrices our used with problems that we are familiar with. and we introduce matrix inverses.

Matrix Algebra Part 2
Properties of Matrix Arithmetic and Matrix Transposes Reading
7 pages

In this lecture, we go in depth with the importance of elementary matrices. They are used to evaluate inverses and to get matrices into RREF form. It turns out that they are useful with determinants too, but that's for later...

Elementary Matrices

It's hard to find a nice systematic way to compute a matrix inverse. Good news is, there is one. Hint: It's in this lecture.

Preview 04:29
Inverse Matrices and Elementary Matrices Reading
10 pages
Finding Inverse Matrices Reading
11 pages
Special Matrices Reading
7 pages
LU Decomposition Reading
7 pages
Systems Revisited Reading
10 pages
Chapter 1 Homework
1 page

Computing the determinant of a matrix is a pain. In this lecture, we see some fast ways of computing them for any square matrix.

Determinants of a Matrix
The Determinant Function Reading
10 pages
Properties of Determinants Reading
7 pages
Method of Cofactors Reading
9 pages

Determinants barely change if you RREF a matrix. Here we prove why, and we show the fastest way of computing a determinant.

Preview 12:07

So we've learned how to find determinants, but why are they useful? Find out in this lecture.

Properties of Determinants Part 2
Using RREF For Determinants Reading
9 pages
Cramar's Rule Reading
4 pages
Chapter 2 Homework
1 page
+ Vector Spaces and Linear Transformations
21 lectures 01:57:22

Vector spaces is that part of linear algebra where people tend to lose their minds. This is good because abstraction does that. Here I want to define linear spaces.

Examples of Vector Spaces

In this lecture, we cover the official definition of vector spaces via the 8 axioms.

Axioms of Vector Spaces
Vector Spaces Reading
13 pages

In this lecture we take 5 seconds to define a subspace. Then we go into tons of examples.

Subspaces Part 1

More examples!

Subspaces Part 2
Subspaces Reading
9 pages
Span Reading
9 pages

There are some different interpretations of how to determine linear independence. In this lecture, we cover all of them.

Linear Independence
Linear Independence Reading
11 pages

It's weird how infinite spaces can be defined by a couple of vectors. Here we go through what dimension is and show an example of a space that is infinite dimensional.

Preview 12:15
Basis and Dimension Reading
16 pages

This lecture is generally a hard one to grasp, but I will try to make it simple and easy to understand.

Change of Basis
Change of Basis Reading
13 pages
Fundamental Subspaces Reading
12 pages
Chapter 3 Homework
1 page

Now that we know what space is, let's manipulate space with functions, but not just any types of functions...

Introduction to Linear Transformations Part 1

In this lecture, we continue the exploration of linear transformations.

Introduction to Linear Transformations Part 2
Linear Transformations Reading
11 pages
Examples of Linear Transformations Reading
9 pages

Matrices... linear transformations... What's the difference? None.

Matrix Representations of Linear Transformations
Chapter 4 Homework
1 page
+ Orthogonality, Norms and Inner Product Spaces
14 lectures 01:15:26

Let's revisit Pre-Calc and Vector Calc.

The Scalar Product (AKA Dot Product)
Vectors Reading
15 pages
Dot Product and Cross Product Reading
14 pages
Euclidean n-Space Reading
11 pages

We construct the perp space and define it.

Orthogonal Spaces

If anything can be taken away, it's this. This is the most applicable lecture you will ever see.

Least Squares Problem
Least Squares Reading
9 pages

Everything you know is a lie... again... Let's redefine the dot product so that you can use it with anything.

Inner Product Spaces
Inner Product Spaces Reading
8 pages

So you thought the Taylor series was cool? This is even better!

Projections Application

These sets create nice geometries and makes math simple.

Orthonormal Sets

Most formulas of this process are long and annoying. Let's make it sweet, short and to the point. We cover some examples and then do some applications with it. If you don't know this process, you will after this lecture.

Orthonormal Basis Reading
13 pages
Chapter 5 Homework
1 page
+ Eigenvalues
4 lectures 18:02

Let's learn about a topic that has so much application everywhere, but nobody understands why.

Eigenvalues and Eigenvectors

Here is a solid example of eigenvectors that involve imaginary numbers.

Complex Eigenvectors and Eigenvalues
Chapter 6 Homework
1 page
Eigenvectors and Eigenvalues Reading
31 pages
+ Conclusion
1 lecture 02:33