That's the dot product.

If you're familiar with dot product, it's essentially the dot product of these two matrices.

I take the dot product, right?

Dot, dot, dot, dot.

I don't want to go into the whole dot dr and take the dot product over and over again.

Well this guy is just the dot product of this with itself.

It's the dot product of the force and our super small displacement.

And we'll see that the dot product is actually not so crazy.

You know, dot, dot, dot.

And dot dot dot is also a dot.

The position before it dot dot dot well dot dot dot becomes a dot in the middle.

Dot x dot says change the middle to an x. x dot dot, change the middle to an x dot dot dot again, middle is a dot dot dot dot, middle is a dot dot dot and then the first one is the last one here so dot dot dot again is a dot.

So we actually can take the dot product or we can multiply these two.

I think you can see that this is the dot product of two vectors.

Dash Dot Dot

Cisco Dot Dot

Year 1, 2, 3, dot, dot, dot, dot, 9, 10.

So, we could start off with the same input as before, which was, dot dot dot x dot dot dot dot.

Remember, we are looking down here. dot x dot, That's number 4, is an x. x dot dot is a dot. dot dot dot is an x. and dot dot dot is an x, as well.

Now we have dot dot x, and dot dot x, that's number two here, gives me an x. dot x x is an x, x x x is a dot. x x dot, is a dot. x dot dot is an x. dot dot dot, is a dot.

And I've done multiple videos of this, in the linear algebra playlist, in the physics playlist, where I talk about the dot product and the cross product and all of that, but this is the dot product of the vectors d and f.

So that's equal to the dot product of our force and our super small displacement.

Just the way we have defined our multiplication, or the dot product, can we multiply?

We had vectors here, but when you take a dot product, you just get a number.

And if the dot product is a completely foreign concept to you, might want to watch, I think I've made multiple, 4 or 5 videos on the dot product, and its intuition, and how it compares.

So when we have a dot at the beginning, its neighbor on the left is a dot, and its neighbor on the right is a dot, we have dot dot dot, and that's replaced with an x. dot dot dot again, is an x. dot dot x, is a dot.

Now at the ends we want to link around so this dot here has to its left a dot and to its right a dot, so we have dot dot dot again and dot dot dot says change the middle to a dot.

Dot

Dot

But just to give you a little bit of that intuition right here, the dot product, when I take f dot d, or d dot f, what it's giving me is, I'm multiplying the magnitude, well

And so after five generations, we have the string dot dot dot x x dot x x.

One, one, point zero zero one, zero zero one, dot dot dot.

This means 1 2 3 plus dot dot dot, up to n.

For this question I'm going to explain how we take an input string, which in this case is dot dot dot x dot dot dot dot, and we change it according to some rules.

Dot Game

Atra Dot

Dot spacing

Dot size

Dash Dot

Strip dot

Add dot

DOT. END

The dot!

That means were going to replace dot dot dot, the middle element by an x.

DOT was named after the 8 bit dot, OK?