Find the transformation matrix

How to find the transformation matrix in MATLAB?

For example:

x1=[1;2];

x2=[4;5];

y1=[3;4];

y2=[2;1];

y1=S*x1;

y2=S*x2;

where S=[s1 s2; s3 s4]

Which function will help you find S?

upd №1: I know how to do it on a piece of paper. But maybe there is a standard function in MATLAB.

Answer 1

[John D'Errico]

First, learn to use matrices, NOT numbered variables. Assuming that you have a matrix X, and a matrix Y, with x1 x2, y1, y2 as columns...

x1=[1;2];
x2=[4;5];
y1=[3;4];
y2=[2;1];

X = [x1,x2];
Y = [y1,y2];

then ONLY if the matrix X is non-singular does a solution exist. So is X singular? It must be of full rank if it is non-singular, or a small condition number.

rank(X)

ans = 2

cond(X)

ans = 15.2678

So X is non-singular. In that case,

format long g
S = Y/X

S = 2×2

-3.66666666666667 3.33333333333333 -6 5

Does S work? Of course. I could also have written it as S = Y*inv(X), but Y/X is a better choice in MATLAB.

norm(Y - S*X)

ans = 
      1.83102671940889e-15

So effectively zero, only floating point trash remains.

[reincornator]

I know how to do it on a piece of paper. But maybe there is a standard function in MATLAB.

[Bjorn Gustavsson]

Have you even bothered trying the provided solution?

>> y1-S*x1 

ans =

   1.0e-15 *

    0.4441
         0

>> y1-S*x1 

ans =

   1.0e-15 *

    0.4441
         0

Clearlty the provided solution solves your problem.

[reincornator]

I was wrong. Thanks.

[John D'Errico]

I showed how to use what IS the standard function in MATLAB.