Linear Algebra Math Made Simple: The Study of Spaces
4.6 (74 ratings)
1,186 students enrolled
Wishlisted Wishlist

# 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)
1,186 students enrolled
Created by Kody D'Amours
Last updated 4/2015
English
Current price: \$10 Original price: \$20 Discount: 50% off
30-Day Money-Back Guarantee
Includes:
• 5.5 hours on-demand video
• 36 Supplemental Resources
• 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
Requirements
• Algebra from high school
• For inner products sections, we will give examples involving integrals...
Description

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
Students Who Viewed This Course Also Viewed
Curriculum For This Course
69 Lectures
11:30:11
+
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.

Introduction
02:26

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
12:42
+
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
08:57

14 pages

20 pages

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

Reduced Row Echelon Form Part 1
11:33

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

Reduced Row Echelon Form Part 2
11:44

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
08:14

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

Matrix Algebra Part 1
11:31

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
13:09

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
04:29

Inverse Matrices and Elementary Matrices Reading
10 pages

11 pages

7 pages

7 pages

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
08:59

10 pages

7 pages

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
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
06:12

9 pages

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
14:34

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

Axioms of Vector Spaces
07:40

13 pages

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

Subspaces Part 1
13:06

More examples!

Subspaces Part 2
13:21

9 pages

9 pages

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

Linear Independence
17:48

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
12:15

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
09:51

13 pages

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
10:44

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

Introduction to Linear Transformations Part 2
11:52

11 pages

9 pages

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

Matrix Representations of Linear Transformations
06:11

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)
07:15

15 pages

Dot Product and Cross Product Reading
14 pages

11 pages

We construct the perp space and define it.

Orthogonal Spaces
06:14

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

Least Squares Problem
12:44

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
11:17

8 pages

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

Projections Application
11:27

These sets create nice geometries and makes math simple.

Orthonormal Sets
08:21

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

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
11:27

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

Complex Eigenvectors and Eigenvalues
06:35

Chapter 6 Homework
1 page

31 pages
+
Conclusion
1 Lecture 02:33

CONGRATS!!!

Conclusion
02:33