rotation matrix between two coordinate systems matlab

I have a coordinate system A

Example: 3 principal vector direction of system A are:

e0=  [0.3898  -0.0910   0.9164]    
e1=  [0.6392   0.7431  -0.1981]
e2=  [-0.6629  0.6630   0.3478]

And, I have a cartesian coordinate system B with three unit vector

    nx=[1 0 0]  
    ny=[0 1 0] 
    nz=[0 0 1]

How can i find transformation matrix between two coordinate systems A & B ?

[Güinther SAIBRO]

I didn't understand why do you need the last space vectors with you already have the transformation matrix.

If you are trying to do a space transformation from R^n to R^m you just need a m x n matrix and to multiply this matrix to a column vector in R^n.

In your case, you can write:

A= [0.3898 -0.0910 0.9164; 0.6392 0.7431 -0.1981; -0.6629 0.6630 0.3478];

P = [ [x'1;y'1;z'1] [x'2;y'2;z'2] ... ] % The idea is that you need column vectors of x,y and z.

and just P_R3 = A*P;

I believe that this can solve your problem.

[ha ha]

sorry. Please see "edit question"

Answer 1

[Jan]

E = [e0; e1; e2]

is the transformation matrix already for the rotation. There seems to be a translation of the origin in addition, such that you need to add this vector afterwards also.

[ha ha]

i think my question is not clear. Please see my new question:

 https://jp.mathworks.com/matlabcentral/answers/357494-how-to-find-rotation-matrix-from-vector-to-another