Row vector divide by row vector

Question

Jimmy Zhan 2020-7-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/572440-row-vector-divide-by-row-vector

编辑： Bruno Luong 2020-7-31

采纳的回答： Bruno Luong

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.

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Answer 1

Bruno Luong 2020-7-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/572440-row-vector-divide-by-row-vector#answer_472627

编辑：Bruno Luong 2020-7-29

在 MATLAB Online 中打开

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)