There isn't a "difference" between the pseudoinverse and the inverse. The pseudoinverse is just a generalization of the inverse — it tries to do the same job. The pseudoinverse A+ strives to satisfy A·A+ ≈ Ɪ, where Ɪ is the identity matrix.
If the inverse doesn't exist, the pseudoinverse is the closest we can get to the inverse.
If the inverse exists, the pseudoinverse is exactly equal to the inverse.
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