Slope

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

That's the slope of the slope, or the rate of change of the slope itself.

The sloping roof.

Independence.

linear regression.

The slope was increasing.

Slope decreases.

They have come to the top of a cliff.

Use linear mode

Linear middle of the distribution

It's a linear combination of the columns.

So our slope has decreased.

Slope is decreasing.

The slope was very positive.

The rate of change of the slope is negative.

Throw me off the cliff!

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

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

One, they said, Life is on an incline.

We made the last one. I know.

Yes, for over there on the steep side.

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.

So what did we say about concave upwards? concave upwards is when the slope is increasing, which means that the rate of change of the slope is positive.

If the slope is constantly increasing, then the rate of change of slope is positive, then the second derivative is positive.

If the slope is decreasing, then the rate of change of slope is negative, which tells us that the second derivative is negative.

If only we had some sort of ramp... ding

So as we increased x, the slope increased.

And as we increase now, our slope becomes negative.

Our slope was decreasing up until this point.

Now, in concave downwards, the slope is decreasing.

A time when you can't tell between the road and a cliff.

It would have been so easy. Remember the precipice?

There are dizzy daffodils on the hillside

Then we come to the rapids?

Hendricks and his men are headed for the rapids.

Fiske, Vicente, watch that end of the ridge.

You spawn of the devil's own strumpet!

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

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.