I have two coordinate systems, like so
How can I transform a point on the one of the coordinate system to other ?
Pxyz = M . Px'y'z' what is M ?
From the image it looks like both your coordinate systems are cartesian coordinates, where the only difference between the two is that one has a different origin from the other.
If this is the case then to translate from
Where [dx, dy, dz] is the difference between the origins of the two coordinate systems.
Matrix multiplications always have the origin as a fixed point and so you can't perform translations using a 3x3 matrix, however as a sort of workaround you can express your 3-dimensional coordinates as the 4-dimensional vector
You can then ignore the 4th component to get the translated 3D coordinates. See more on Wikipedia here