Projection Matrix - Horizontal Perspective, Vertical Orthographic

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Is it possible to create a projection matrix that is horizontally perspective, yet vertically orthographic? I am trying to create a game in Unity (2D) and am just learning about projection matrices. If you look at an engine like Construct 2, it has this capability baked in by default (as you can set parallax based on the x and y axis). Now, I know this can be done with an orthographic camera and scripts to move the backgrounds, but I was wondering if it can be done with a perspective camera.

Thanks!

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