How to perform the conversion of (r,v) vector from ECEF to ECI (J2000) coordinate frame?
What I tried
I multiplied the matrix ([cosA -sinA 0] [sinA cosA 0] [0 0 1]) by the state vector, where A is Greenwitch mean sidereal time.
This equation shows that the Z axis doesn't change. However, I have the ephemeris of a real satellite in both coordinate frames, and there Z axis differs! Where is the issue?