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How does resizing an image affect the intrinsics?

Hi there, i have calibrated a camera using images at 1280 * 720. the intrinsic data is:

  1280 720</cameraResolution>
<camera_matrix type_id="opencv-matrix">
    6.5700301862152855e+02 0. 6.4669706479436286e+02 0.
    6.5700301862152855e+02 3.4711751174913059e+02 0. 0. 1.</data></camera_matrix>

So the focal length is:


and the center pixels are:

cx = 646.69706
cy = 347.11751

Now, to speed up my algorithm, I have resized the images by half, to give a resolution of:


My question is, how do I need to adjust my intrinsic matrix to match? I assume i need to half the cx and cy values, but the focal stays the same? Is this correct?

Thank you.