So, it's W transpose times C transpose times CV.

So this thing right here is going to be equal to X transpose, C transpose.

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13 FS (4 FSb),

Now, we also know that A times B transpose is the same thing is B transpose, A transpose.

Let's take the case in particular of A transpose A. A transpose A is going to be equal to what?

X transpose times C transpose. And then you have that times CX.

(59 posts)

The transpose of this matrix is equal to the inverse.

That's A transpose.

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And what is it A transpose equal to?

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For a typical 20 m3 insulated tank

Then C inverse is equal to C transpose.

The second column here is going to be v2 transpose.

And of course its inverse is going to be the transpose of that.

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But clearly this is a much, much simpler way of finding a projection than going through this mess of saying A times the inverse of A transpose A, times A transpose I forgot that A transpose when I wrote it the first time times x.

Returns the transpose of a matrix, i. e. rows and columns of the matrix are exchanged.

This is the same thing is taking one of their transpose times the other one.

So this is going to be equal to X transpose X.

A transpose A is going to be k by k.

So it's just going to be the transpose of this thing. So I'll write another 1 3 out here, just to simplify things.

I need to multiply that times A transpose. A transpose is just going to be 1 3, 2 3, 2 3, 1 3, and then 2 3, minus 2 3.

And now we know that C transpose is the same thing is as C inverse.

But to find the transpose of a 10 by 10 matrix, a lot easier.

The dot product is equal to the transpose of one guy as kind of a matrix times the second guy.

This is the same thing as y transpose, if you view them as matrices, y transpose times y. y transpose y is just y1, y2, all the way to yn times y1, y2, all the way to yn.

So this is equal to CW transpose times CV. And all of that over these lengths.

We've already seen that the transpose of this matrix is the same thing as the inverse of this matrix.

That's the identity matrix, and this is going to be equal to W transpose times V over the products of their lengths.

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X transpose is the same thing as X dot X which is the same thing as the length of X squared.

Well each of these columns are going to become rows. So the first row here is going to be v1 tranpose.

So this simplifies to the projection onto V of our vector x, simplifies to A times the inverse of the identity matrix It was just the identity matrix. So it's just A times Ik, times A transpose I always forget that second A transpose right there times x.

Then you're going to go all the way down. The kth column there is going to be to vk transpose.

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So it's just equal to A times A transpose, times x, which is a huge simplification.

I still have to do a matrix product, but finding the transpose of a matrix is pretty straightforward.

I hope you already appreciate that this is a lot less painful than we had to take A transpose A, and then inverse it in between.

Added to this amount is a carry over of 5 million from the unspent allocation of prior years, and a transfer of 11 million to the operational reserve, thus leaving an amount of 600 million of projected income and expenditure for the 1994 1995 biennium.

So you re looking here at one of the first printed books using movable type in the history of man, 550 years ago.