Examples of using Matrix representation in English and their translations into Thai
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Colloquial
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Ecclesiastic
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Ecclesiastic
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Computer
And this guy's matrix representation is c.
And then we're going to take the product of that with this guy's matrix representation, which is a.
That is the matrix representation of this transformation.
Then, what's the transformation T, what's it's matrix representation going to be.
So its entire matrix representation is going to be guy's matrix times this guy's matrix. .
And then you take that matrix, and you take the product-- so this guy's matrix representation is a b, right?
Given this we can use our matrix representations to replace this kind of transformation representation. .
Now, this is an interesting thing, because we were able to figure out the actual matrix representation of this composition transformation.
I said that the matrix representation of our linear transformation is going to be an m by n matrix. .
In the next video, I will actually show you how to figure out a matrix representation for this, which is essentially a transformation.
So the matrix representation of the entire composition is going to be this matrix times this matrix. .
Where we can say A is its matrix representation times a vector x.
So the matrix representation of this whole thing is this guy, taking the product of a b, and then taking the product of that with c.
And that will create a new matrix representation which you can call C.
Now to figure out C, the matrix representation of our transformation, all we do is we apply the transformation to each of these columns.
Because then we could say that the composition of T with S of x is equal to the matrix representation of B times a matrix representation of S.
Linear transformations, and their matrix representation will be that right there.
But the really neat thing here is, and I think this will really hit the point home, that the matrix representation is just one way of representing multiple types of problems.
And then the neat thing about this, if you were to just write this out in its matrix representations-- we did this in the last video-- this would be equal to the S matrix A times this vector right here, which is Bx.
But the real learning, and the big real discovery of this whole video, is to show you that the matrix representation can represent multiple different problems.