Examples of using Row vector 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
You now get a row vector.
We could call them row vectors maybe. r2, I'm not doing it too formally.
And really, all this is, is a row vector.
I could do it maybe for row vectors, but we don't need to make a new definition.
These are vectors now, row vectors.
So the dot product of this row vector with this column vector should be equal to that 0.
This is actually called a row vector.
We multiply this row vector times this column vector to get row 1, column 2, right?
Like, like a row vector.
If this is a column vector before, now it's going to become a row vector.
So I'm going to multiply this row vector times this column vector. .
So this is essentially the dot product of this row vector.
I haven't formally defined a row vector times a column vector. .
Actually, this just looks like a vector, it's just a row vector.
We haven't really defined operations on row vectors that well yet, but I think you get the idea.
Like we have been working with, I can write my matrix as each row is the transpose of a column vector, or it's a row vector.
Now instead of viewing these as row vectors, we could view.
And so this term, it will be this row vector times this column vector-- let me do that in a different color-- will be 1 times 6 plus 2 times 8.
So we could also view this as the span of the row vectors of our original guy.
We called the row vectors of those matrix, we called them the transpose of some column vectors, a1 transpose, a2 transpose, all the way down to an transpose.
And then the second entry is going to be the dot product of this row vector with this column.
In fact, not so many videos ago I had those row vectors, and I could have just called them the transpose of column vectors, just like that.
We're taking each row and we're essentially taking the dot product of this row vector with this column vector. .
Well, if all of these guys can be represented as linear combinations of these row vectors in reduced row echelon form-- or these pivot rows in reduced row echelon form-- and these guys are all linearly independent.
If you have the transpose of-- we can view this as, even though it's a transpose of a vector, you can view it as a-- it is a row vector, but you could also view it as a matrix.
And we can actually take the dot product of this row vector and this column vector because they have the same length.
I say essentially because I didn't define a row vector dot a column vector. .
Or you can interpret it as, essentially, the dot product of the row vectors, or you could define the row vectors as a transpose of column vectors. .
And just to kind of keep things a little simple, let me just define-- just for notational purposes, you can view these as row vectors if you like, but I haven't formally defined row vectors so I won't necessarily go there.
And you're going to keep doing that because all of these are, essentially,-- you can kind of view it as the dot product of-- I haven't defined dot products with row vectors and column vectors, but I think you get the idea-- the sum of each of these elements, multiplied with the corresponding component in this vector.