MATLAB: How does Matlab divide two row vectors by each other to get a scalar

divideMATLABrowscalarvectors

Let's consider, A is a vector like shown:

A = [20 30 40];

and B is also a vector:

B = [5 10 20];

when you want to execute this operation:

C = B/A;

then you will get a scalar: 0.4137

if you want to check this answer by doing this:

C.*A

It should be got B again but you will get this vector instead:

ans =

8.2759 12.4138 16.5517

Could somebody explain what's going on?

To expand slightly on that, ‘C’ is the least-squares estimate of the slope of

with the y-intercept forced through the origin:

figure
plot(A,B,'p',  A,C*A,'-r',  [0 A(1)],C*[0 A(1)],':k')
axis([0  45    0  25])

If your data are column vectors x and y and your model is

y=m*x+b

then the solution for b would simply be

b_fit = mean(y-m*x);

C = A / B determines the matrix C such that:

C * B = A

Try it:

A = [-1;1;7];
B = [5;7;-2];
C = A / B;
C * B

>> [-1; 1; 7]