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What is A/B when A and B are 1x3 row vectors

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Ashish Sheikh
Ashish Sheikh 2015-3-7
编辑： Matt J 2015-3-8
This is so simple...i think i'm missing some thing
What is the result of A/B ???? (if A and B are same length row vectors)
ex: A=[1 2 3]; B=[4 5 6];
A/B in MAtlab gives me 0.4156

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Matt J
Matt J 2015-3-7
编辑：Matt J 2015-3-8
I want to know how this gives me 0.4156 ??? A/B is A*inv(B) ....
A/B is always defined as the least squares solution to the equation,
A=X*B
or
min. f(X) = norm(A-X*B)
In this case, the solution X has to be a scalar, since that is the matrix shape that can be left multiplied with B to produce another 1x3 matrix A. You can readily confirm that X=0.4156 is the minimizing value by plotting f(X),
>> fplot(@(X)norm(A-X*B),[0.41,.42])

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Star Strider
Star Strider 2015-3-7
编辑：Star Strider 2015-3-7
You’re likely not missing anything other than an slightly more inclusive interpretation of that operation. You’re doing a linear least-squares fit through the origin on ‘A’ as a function of ‘B’.
To illustrate symbolically:
A=[1 2 3]; B=[4 5 6];
P = A/B; % ‘P’ = Parameter ‘Vector’ (1x1 Here)
R = P*B; % Regression Line
figure(1)
plot(B, A, 'p') % Plot Data
hold on
plot(B, R, 'LineWidth',1.5) % Plot Regression
plot([0 4], P*[0 4], '--r') % Extend To Origin
hold off
axis([0 8 0 4])
grid
and to illustrate literally:
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Ashish Sheikh
Ashish Sheikh 2015-3-7
编辑：Ashish Sheikh 2015-3-7
Thanks @Star strider ....Now i got it ,...
Star Strider
Star Strider 2015-3-7
My pleasure!
You can now Accept two answers, if you want to Accept mine as well.

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