As the equation above illustrates, DICOM only specifies image plane I and J axis directions. Applications often define a third (K) axis. For a single plane, you can always choose this K axis direction so that IJK axes form an orthogonal basis. However, you do not have the freedom of choosing arbitrary K axis direction if you want to describe geometry of a gantry-tilt multi-slice volume with a single 4x4 matrix. See for example this FAQ and computation of the shear matrix.
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