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Linear Algebra Math Made Simple: The Study of Spaces

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Learn How to Define Space And How it is Characterized And Measured. We Make Linear Algebra Math Fun And Easy.

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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

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

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Curriculum For This Course

Expand All 69 Lectures
Collapse All 69 Lectures
11:30:11

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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

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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

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

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

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

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

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

08:59

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

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

Using RREF For Determinants Reading

9 pages

Cramar's Rule Reading

4 pages

Chapter 2 Homework

1 page

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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

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

13:06

More examples!

Subspaces Part 2

13:21

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

17:48

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

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

09:51

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

10:44

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

Introduction to Linear Transformations Part 2

11:52

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

06:11

Chapter 4 Homework

1 page

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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

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

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

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

11:17

Inner Product Spaces Reading

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

Orthonormal Basis Reading

13 pages

Chapter 5 Homework

1 page

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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

Eigenvectors and Eigenvalues Reading

31 pages

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Conclusion
1 Lecture
02:33

CONGRATS!!!

Conclusion

02:33

About the Instructor

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.

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