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

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SUMMARY

The discussion centers on determining the 4x4 operator matrix O that transforms a 4x1 vector A into another vector B. Given A = [0.7; 0.4; 0.4; 0.3] and B = [0.74; 0.56; 0.08; 0.36], the unique identification of O requires results from three additional linearly independent vectors. The basis vectors provided are [1; 0; 0; 0], [0; 1; 0; 0], and others, which can be utilized to derive the operator matrix O through linear transformations.

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