Master Linear Algebra 2020: The Complete Study Of Spaces

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.

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

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

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

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.

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

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

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...

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.

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

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

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.

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

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

More examples!

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

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.

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

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

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

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

Let's revisit Pre-Calc and Vector Calc.

We construct the perp space and define it.

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

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

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

These sets create nice geometries and makes math simple.

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.

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

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

CONGRATS!!!