How to do foward right division?

I have an array of A (1x182) and B (1x182). When I use C=A/B; it gives one single number. How did Matlab get that single number?

I understand if I use ./ I will get C=(1x182).

[Stephen23]

To use MATLAB properly you need to read and understand this page:

http://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

Answer 1

[Guillaume]

The / operator ( mrdivide) is particular to matlab. It solves a system of linear equations. In your particular case, it finds x such that x*B = A (note the reversal of the order of A and B) using the least square method, so it basically performs a linear fit between A and B with the added constraint that the line goes through the origin.

The traditional division is always ./ ( rdivide)

Answer 2

[Star Strider]

As I did my best to explain in my Answer to your earlier Question How to find a the scale of two data?, the mrdivide function solves the matrix division problem in a least-squares sense.

You can get the same result by solving the least-squares equation:

S = sum((B - scale*A).^2)                                   % Least Squares Equation
dS/dscale = -2*sum((B - scale*A)*A)                         % Take Derivative w.r.t. ‘scale’
dS/dscale = -2*sum((B.*A - scale*A.^2)                      % Distribute
dS/dscale = -2*sum(B.*A) - scale*sum(A.^2)                  % Simplify
sum(B.*A) = scale*sum(A.^2)                                 % Set Derivative To Zero And Rearrange
scale = sum(B.*A) / sum(A.^2)                               % Solve For ‘scale’

NOTE: Do not run any other than the last line of that code! It describes an algebraic derivation of the least-squares estimator for ‘scale’, and will throw a number of errors if you try to run it.

So using the vectors in your previous Question:

A=[0.46,-0.51,1.02,-1.02,1.55,-1.55,2.06,-2.06,2.02];
B=[0.09,-0.13,0.32,-0.29,0.38,-0.41,0.48,-0.56,-0.36];

scale_rdivide = B/A
scale_leastsquares = sum(A.*B) / sum(A.^2)

scale_rdivide =
   169.1133e-003

scale_leastsquares =
   169.1133e-003

Answer 3

[Torsten]

C=(A*B.')/(B*B.')

Best wishes

Torsten.