learned linear algebra.

Well actually, not algebra, some linear algebra.

linear algebra will find it.

In linear algebra, linear transformations can be represented by matrices.

linear algebra, and I'm Gilbert Strang.

So that when you see in your linear algebra book, when you see linear algebra problems, when you see this big capital

I actually prove it in the linear algebra playlist.

And we'll do more of that in linear algebra.

In linear algebra, you can apply it to anything.

But in linear algebra, we like to be general.

The concept of linear combinations is central to linear algebra and related fields of mathematics.

There's a lot of names and labels in linear algebra.

It only makes sense that we have something called a linear transformation because we're studying linear algebra.

You have a system of linear equations which is Algebra I.

But in linear algebra, this is one of the few subjects where

The text for the course is this book, Introduction to Linear Algebra.

The fundamental problem of linear algebra, which is to solve a system

And the word image is used more in a linear algebra context.

If anything, in linear algebra, the field, or the gods of linear algebra, are kind of experts in to some degree stating simple and obvious things in convoluted and Byzantine ways.

I'm not looking at the comment right now, but if I remember correctly, they said their linear algebra teacher said that linear algebra is the art of choosing the right basis.

There's even a branch of mathematics that uses matrices constantly, called Linear Algebra.

And if you're doing this in you Algebra 1 or your Algebra 2 class you're probably using it to represent linear equations.

Would any of you complain if this was the case about doing linear algebra?

I have linear algebra, science, physics, even nowadays, chemistry and biology, as you've seen.

History The study of linear algebra first emerged from the study of determinants, which were used to solve systems of linear equations.

But this is, I think, a really good toe dipping for linear algebra as well.

If you ever get a chance to study Linear Algebra, do it, it's pretty awesome.

But the whole study of linear algebra is abstracting these ideas into multi dimensional space.

One term you are going to hear a lot of in these videos, and in linear algebra in general, is the idea of a linear combination.

Remember what rn was. rn we defined way back at the beginning of the linear algebra playlist.

They're actually at least a useful notation to use as we progress through our explorations of linear algebra.

linear algebra is someone will write they won't just write the set of all real numbers, they'll write Rn.

In this first, what I'll call this is my first real linear algebra video, I want to introduce you to some concepts that you're going to see over and over in linear algebra, and if they're not introduced to you properly in the beginning, they can be very confusing.

Uhm, if you take linear algebra and calculus your professor might use those terms and it's good to be familiar with it.

that you get kind of used to in linear algebra. Even though you can't really visualize it, you sort of think you

linear algebra books I looked at, they didn't specify this but you can kind of view this as the range of T.

In linear algebra, an alternant matrix is a matrix with a particular structure, in which successive columns have a particular function applied to their entries.

Now I will show you another application of matrices that actually you're more likely to see in your linear algebra class when you take it in college.

And in the terminology that you don't normally see in linear algebra a lot, you can also kind of consider it its range. The range of T.

Algebra type

Algebra courses.

Algebra, science

And my sense of why, in the linear algebra world, they use this, is because you kind of imagine that this vector is being changed into that vector.

If you don't remember how to do this you should probably review the level one and level two linear equations lectures that I have in the algebra playlist.

Further down, you start getting into pre algebra and early algebra.