Simplex basis

For standard-form linear programming constraints $Ax=b$ of full row rank, a simplex basis is a set of columns forming an invertible square matrix $B$. The remaining variables are nonbasic; setting them to zero gives the basic solution $x_B=B^{-1}b$. It is feasible if these basic variables are nonnegative. A pivot exchanges one basic and one nonbasic column while maintaining this representation.