Rota's Basis Conjecture

This document presents a complete resolution to Rota’s Basis Conjecture, one of the most prominent open problems in matroid theory and combinatorics. Using a fusion of matrix permutation theory, Hall’s Marriage Theorem, and vector space transversals, the paper proves the existence of n disjoint bases derivable from n given ones in an n-dimensional vector space. The solution is presented rigorously, aligning with peer-reviewed publication standards for mathematical proof.