The transpose of this matrix is equal to the inverse.

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

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

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

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)

That's A transpose.

Transferred over from Fort Shafter.

Prewitt. Transfer from Fort Shafter.

And what is it A transpose equal to?

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And if we construct A in that way, then the projection of x onto V, this linear transformation can be represented as A times A transpose times x.

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Then C inverse is equal to C transpose.

So you immediately see that the determinant, or hopefully you immediately see, that the determinant of X plus the determinant of Y is equal to the determinant of Z.

So the matrix representation of the entire composition is going to be this matrix times this matrix.

The second column here is going to be v2 transpose.

We just multiplied this matrix times this matrix.

This guy and this guy add up to this guy.

And then if I were to do this guy and this guy, add up to that guy. Let me do another one. And then finally that term plus that term add up to that term.

This matrix right here will become that matrix right there.

matrix

Matrix

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

But I have left you a book, revealed by god,

Now, the determinant of B, you could view as the determinant of this guy.

So its entire matrix representation is going to be guy's matrix times this guy's matrix.

It's not the case let me write what is not the case so not the case that if Z is equal to X plus Y, it is not the case that the determinant of Z is necessarily equal to the determinant of X plus the determinant of Y.

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.

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.

I want to be very clear, Z is not X plus Y.

And by the matrix, I mean literally the matrix, like the movie The Matrix.

This is our transformation matrix S. This is our matrix A.

So the inverse of matrix a is equal to 1 over the determinant of a times the adjugate, or adjoint, of matrix a.

Matrix size

Amended Matrix