Recursive "pinv" function?

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PSF
PSF 2019-3-28
Has a recursive version of the "Moore-Penrose Pseudoinverse" function ("pinv") ever been done in Matlab?
Say for instance, I've got two inputs x1 and x2, where
x1 = [1 1]
x2 = [1 2]
If I do the pinv of x1, pinv(x1), I get an output of:
0.5000
0.5000
Including the other input, x2, like if I did,
T = [x1; x2] , and then did, pinv(T), I get an output of
2.0000 -1.0000
-1.0000 1.0000
Using just the result of pinv(x1) and the second input, x2,
would it be possible to get the same result as as pinv(T)?
It seems the theory for a recursive Moore-Penrose Pseudoinverse exists (here) and it would be helpful to know if there had been any Matlab code implementation publicly available.

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