Row vector divide by row vector
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Can anyone explain what is the mathematical operation for C = A/B where A and B are both row vectors?
>> A = [1 2 3 4]
>> B = [2 2 2 2]
>> C = A/B
C =
1.2500
As you can see, C*B is not equal to A. This suggest that / is not a matrix right division. It almost looks like / is the average of elementwise division between two row vectors.
采纳的回答
Bruno Luong
2020-7-29
编辑：Bruno Luong
2020-7-29
It returns the scalar C (maxtrix 1x1) such that
C*B ~ A
in the sense that
norm(C*B - A)^2 % or equivalently
sum((C*B - A).^2)
is minimal.
Illustration:
>> sum((C*B-A).^2)
ans =
5
>> sum(((C+0.1)*B-A).^2) % move on the right
ans =
5.1600
>> sum(((C-0.1)*B-A).^2) % move on the left
ans =
5.1600
>> ezplot(@(x) sum((x*B-A).^2), [-1 3]) % plot this function, that is a parabola minimum at x=1.25
>> xline(A/B)
1 个评论
Bruno Luong
2020-7-31
编辑：Bruno Luong
2020-7-31
If you want a direct formula, A/B is equal to (applicable for real and complex row vectors)
dot(B,A) / dot(B,B)
or
(A*B') / (B*B')
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