Buckingham PI Theorem proof - Dimensional Analysis

[Grand]

Homework Statement

I am looking for a proof of Buckingham PI theorem in dimensional analysis, but can't really find one anywhere. I saw a proof involving posing the problem as a question in linear algebra, but it was quite unclear.

 

[Coto]

Most books I have found gloss over the proof and fail to incorporate the relevant details.

The closest I have found to a formal proof (in a book) is in Barenblatt's "Scaling, self similarity, and intermediate asymptotics" chapter 0. Otherwise you'll have to look at Buckingham's original paper, "On physically similar systems; illustrations of the use of dimensional equations".