So when we look at that, what we want to then figure out is the market value, the

value to the final private investors who aren't owing something

to somebody else; it's not a company that owns, that's then owned by other people.

That value is then, what's the amount that's held in private, by private

shareholders, so that's C hat ii times Vi.

Now we plug in the Vs here, and we get that V

is equal to C hat times I minus C inverse times P, okay?

So this is a very simple calculation that tells us, as a function of the

underline asset values, what's the value of different companies?

So it's not that a value of different organizations here

in terms of value, interms of valuing their, their actual

owners, is just dependent directly only on their own asset holdings.

But it's going to be dependent on the whole

portfolio of asset holdings, in terms of this factor.

So we'll call this c hat times i minus c inverse.

This is the a matrix. Okay, we'll call it an a matrix.

And what's that doing, Aij tells us, what's the

fraction of the investments owned by organization j that

ultimately accrue to the private shareholders of i, ok?

So lets just look at a very simple example to make this clear.

So suppose there was just two organizations in the world, and

each of them owned half of the shares of the other, okay?

And so here, I'm going to do everything in terms of equity.

You can do this in terms of debt; it gets a little more complicated.

This makes it nice and linear.

So, here, I, you know, each owns half of the assets or,

or investments of the other, and, and some value.

So what's the implied holdings by private investors?

Well, half of, of organization two is held by organization one.

That means that the remaining half is privately-held.

And half of organization one is held by two, and

that means that the remaining half is held privately as well.

So half of the each of the organization is held by

private investors, half is held by the other okay?

So if you do the calculation of what the A

matrix is, it says that ultimately if you this calculation.

That two thirds of the value of the

investments of organization one, actually end up going

to the owners of organization one, and one

third of organization twos' goes to organization ones' owners.

And, and vice versa. Okay?

So let's try and get an idea of exactly what's going on here.

So what this does is that, just on a

very simple matrix analysis which is implicitly capturing the network.