>> It wouldn't be meaningful, right?

I mean Math Lab won't complain at you, it's just 1 3 by 1 plus another 3 by 1.

It gives you an answer.

It gave you what you asked.

It figured you knew what you're doing, of course it's silly Math Lab.

If it only knew, but this is not correct, all right?

So if you actually would numerically evaluate this,

this would come up with something that doesn't mean anything.

And so we really want to be careful that we have apples and apples.

If you add up matrix representations of vectors numerically,

all of the first components should be along the first axis, otherwise, you might

be adding these components with these components, and it makes no sense, right?

So this is very critical that you do this right.

But same thing here.

This is basically just a more compact way.

This is now actually bold for me means a vector, I don't use underscores.

In all the journals you see, the bold is basically a vector these days.

So bold is a vector, if I write it here, I typically have an underscore or

an arrow or something, because I can't do bold with my pen.

But that's an e-frame representation of that vector,

it's a 3 by 1 matrix equivalent to this.

Same thing here.

Same thing here.

This is also, of course,

would be wrong if you would actually numerically evaluate it.

Now halfway through the class I expect you guys to be big boys and girls.

We understand what's going on.

I may write these a few times but then it's implicitly understood

that if you numerically computed this you would be taking a b frame component and

map it into the e frame before you would add them up.

I'm just highlighting.

This is given in the b frame, this is an e frame.

I'm adding them, and I'm saying you guys know what you're doing, right?

You have to get everything into a common frame,

especially when we do the control development.

It just makes things quite a bit shorter.

So you will see this, as we get better and

better at this there's a lot of implied stuff that happens then, too.

Coordinate frames, hopefully very boring.

Coordinate frames you need 3 axis in 3D, given 3-dimensional space.

And the way I typically write the b frame, I have b, 1, 2, 3,

hats to me mean a unit vector.

Very simple, pretty common notation.

If there's an origin, I usually define it as 0 of b,

that's the origin of the b frame.

And you can fully define the frame this way.

It's important you have 3.

It's important that you label what's first, second, third.

That ordering will be critical.

You will see when we get to the rotation matrix and how this gets composed.

Otherwise, again, you end up with stuff in the wrong direction.

So you need to have a notation that tells you what's first, what's second,

what's third.

Right-handed means what?

What should you be able to do with these vectors,

if they satisfy a right-hand rule?