Finding the Matrix O for a 4x4 Operator Acting on a 4x1 Vector

[MrMuscle]

TL;DR

I have a vector A, and when I apply operator O on it, I get vector B.
I know A and B, but don't know how to find O.

I have a 4x4 operator O. I apply it on a 4x1 vector A. Let's say A =[0.7; 0.4 ; 0.4; 0.3]. When O acts on A, I get B.

Let's say B=[0.74 ; 0.56; 0.08 ; 0.36]. The problem is I don't know how to find O. Can you please help me. My basis are [1 ; 0 ; 0; 0], [0;1 ; 0 ;0] ... and so on.

Thanks in advance!

 

[pasmith]

You need to know the results for another three linearly independent vectors in order to determine O uniquely.