Mapping between keypoints in two images using a Homography

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Hi,
I'm sorry if the question seems unrelated; I just had nowhere else to ask.
I have two images im1 and im2 and keypoints from each image – keypoints1 and keypoints2 (matrices of size M1 X 2 and M2 X 2). I also have a homography H which is given by a 3X3 matrix.
Now, I want to map keypoints1 to keypoints2 using H. I want to display im2, the keypoints2 and the transformed keypoints1 on the same figure.
I'm not sure about the mathematics of mapping keypoints1 using H. I can't just multiply them since the dimensions do not agree.
Can anyone please explain to me how to use H to map keypoints1 to correspond to im2?
Thanks in advance,
Gil.

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