And the definition of our linear transformation, or the composition of our linear transformation.

So I can feel the skin.

Independence.

linear regression.

The wasps grabs onto one of the antenna, bites down on it, of the cockroach, and pulls the cockroach.

Their wing is covered with sensors, including sensors that sense deformation of the wing.

It's also an attention sensing system.

It's also an attention sensing system.

Man

The result?

Use linear mode

Linear middle of the distribution

It's a linear combination of the columns.

They have sensors on their wing.

We have amazing antennae.

Each of these has a sensor.

And all a linear combination of vectors are, they're just a

do the linear combinations of the columns fill three dimensional space?

They're able to be moved around by hand, they can sense each other, they can sense their motion, and they have a screen and a wireless radio.

learned linear algebra.

planes, because they're not parallel, they're not special.

So we would be having the linear combinations of nine vectors in

And then I have a final linear transformation f.

And I call it linear change. Unlike cyclical change, when linear change hits we're not going back.

It has a force sensor, so we can tell how hard you're pushing it has motion tracking, so we can tell exactly where you've moved it and it has a vibration sensor, an accelerometer, inside, that detects the shaking back and forth of the tool that lets you know that's a piece of canvas and not a piece of silk or something else.

A linear transformation of x, of our vector x, is the same thing as taking the linear transformation of this whole thing let me do it in another color is equal to the linear transformation of actually, instead of using L,

MV is the linear middle of the distribution.

And that's what's neat about algebra.

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

Let me show you a concrete example of linear combinations.

linear algebra, and I'm Gilbert Strang.

Let's say I have the linear transformation g.

I was also working at a place called the Center for Embedded Network Sensing.

This will verify the sensor connection is good

They can embed sensors and actuators right in the form itself.

We said that if this was the definition of linear independence, or we proved this fell out of the definition of linear independence, and if I have a bunch of vectors, v1, v2, all the way to vn, we say that they are linearly independent.

Linear splines need at least 4 points.

That written statement was filed within the prescribed time limit.

There is a big difference between linear and exponential growth.

And we saw that in our video on linear independence.

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

That's all a linear combination is.

The movement of wind waves can be captured by wave energy devices.

They have antennae that sense odors and detect wind detection.

But they have 40 sensors all over their body.