In Properties of the most diversified portfolio by Choueifaty, he shows that the Most-Diversified portfolio (MDP) has three quantitative properties.
Specifically for duplication invariance, he proves that it exists by stating that "the introduction of a redundant asset leads to a redundant equation in the first-order equations associated to the MDP program" [footnote 17].
I dont really understand how having an extra asset (which changes the covariance matrix) introduce a redundant equation.
I hope someone can clarify my doubts. Thank you!