Row vector divide by row vector

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.

Answer 1

[Bruno Luong]

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)

[Bruno Luong]

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')