Cheap Implementation for the Moore Penrose Pseudoinverse

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Can some one explain Adam W's implementation for finding the Moore Penrose Pseudoinverse?

http://math.stackexchange.com/questions/75789/what-is-step-by-step-logic-of-pinv-pseudoinverse/317053#317053

https://go.helms-net.de/math/divers/ACheapimplementationforthePenrose.htm

I understand the rough Implementation. What is e subscript j? Does it stand for an arbitrary Euclidean Vector?