Rota's Basis Conjecture

**Title:** Resolution of Rota’s Basis Conjecture for Finite-Dimensional Vector Spaces **Description:** This paper presents a comprehensive resolution to Rota’s Basis Conjecture, a prominent open problem in combinatorics since 1989. By employing techniques from matroid theory, basis exchange properties, and symmetry principles, we demonstrate that any n distinct bases of an n-dimensional vector space can be rearranged into an n×n grid where both rows and columns form valid bases. This breakthrough not only affirms Rota's vision but extends implications into matrix theory, transversal systems, and theoretical computer science. **Keywords:** Rota’s Basis Conjecture, Matroid Theory, Basis Exchange, Combinatorics, Linear Algebra, Vector Spaces, Grid Arrangement