Linear Algebra Math Made Simple: The Study of Spaces
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Linear Algebra Math Made Simple: The Study of Spaces

Learn How to Define Space And How it is Characterized And Measured. We Make Linear Algebra Math Fun And Easy.
4.6 (74 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
1,186 students enrolled
Created by Kody D'Amours
Last updated 4/2015
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  • 5.5 hours on-demand video
  • 36 Supplemental Resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
What Will I 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 them
  • Understand linear transformations
  • Understand eigenvectors
  • Understand norms
  • Understand inner products
View Curriculum
  • 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 is the target audience?
  • Potential Engineers
  • Potential Mathematicians
  • Those interested in Algebra
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Curriculum For This Course
69 Lectures
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.

Preview 16:45

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.

Inverse Matrices

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.

Properties of Determinants Part 1

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.

Basis and Dimension

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.

Preview 18:08

Orthonormal Basis Reading
13 pages

Chapter 5 Homework
1 page
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
1 Lecture 02:33


About the Instructor
Kody D'Amours
4.4 Average rating
287 Reviews
5,240 Students
8 Courses
56 Graduate Credits, B.S. Mathematics, Crypto Certificate

Math Should be Fun!  It Should Be Enjoyable And Taught Dynamically!

I love what I teach. I feel like math has a negative connotation to it, and that it is the teacher's job to build enthusiasm and interest through their own passion for the subject. Right now, most students take their math classes just to get the degree requirements - and I respect that - but I also want the student to enjoy what they are learning. This can be hard to do, but I am willing to try my best. When students hit a wall in their mathematics career, then they need someone to help them back up. My goal is to be that person. I have seen how many professors teach, and there are many styles that I like to incorporate. I like to show math in a different and interesting perspective that hopefully is also applicable.