Here, this is a three by four dimensional matrix.

With this notation X2 is a four dimensional vector.

So now I'm going to show you a number of projects that we've built, from one dimensional, two dimensional, three dimensional and even four dimensional systems.

We take this curved 12 dimensional space, and transform it into a flat, four dimensional space.

So this R4 means a set of four dimensional vectors.

Let's look at one more way of representing a four dimensional object.

like a 4 dimensional or 5 dimensional figure.

And that four dimensional space consists of X, Y, Z, and then the yaw angle.

Well, we can do the same thing in the third dimension with a four dimensional object.

We have progressed from a zero dimensional point, to a one dimensional line segment, to a two dimensional triangle.

Sorting multi dimensional array

Insert 2 dimensional vector

Toward the Dimensional Gate.

And the power of Galois' mathematical language is it also allows us to create symmetrical objects in the unseen world, beyond the two dimensional, three dimensional, all the way through to the four or five or infinite dimensional space.

Remember that now this state space is 3 dimensional, not 2 dimensional.

So you can basically program any three dimensional shape or one dimensional, two dimensional up into this chain completely passively.

However, I printed out a 2 dimensional table, not a 3 dimensional table.

Four... Four... Four...

Now when we talk about a three dimensional surface it's a three dimensional surface of a four dimensional sphere that means that any of the three dimensions that are over here on the surface, I can only draw two but that means, if this is true, if the Universe is a three dimensional surface of a four dimensional sphere, that means if you go up and if you just keep going up, you'll eventually come back from the bottom.

This is a four dimensional vector, or a 4 x 1 matrix, and so the result of this, the result of this product is going to be a three dimensional vector.

create scientific 2 dimensional graphs

It's a 3 dimensional state.

It's all very one dimensional.

Here's a 2 dimensional space.

So next, we will talk about two dimensional and three dimensional shapes of ellipticals.

Four... Four?

Four. Four?

So, it works really well for low dimensional problems like 3 dimensional robot localization problems.

Four, plus four, plus four.

A two dimensional vector is needed

This is a 47 dimensional vector.

So it becomes slightly three dimensional.

It's truly a three dimensional space.

This is a three dimensional machine.

Often they are 3 dimensional vectors.

Finally, I copy the 3 dimensional symbol for my policy straight into the 2 dimensional array.

And that's why my training examples are now N dimensional rather N plus one dimensional vectors.

Four times four.

Four, Nan. Four.

Four. She's four.

Four months. Almost four months. Four months.

Obviously this is a 1 dimensional example and not 2 dimensional as the picture suggests over here.

We have a 3 dimensional state space.

It's a thin film, two dimensional existence.

So this is my three dimensional plane.