A Short Proof of Finiteness of Murty's Principal Pivoting Algorithm

@article{Rohn1990ASP,
  title={A Short Proof of Finiteness of Murty's Principal Pivoting Algorithm},
  author={Jiri Rohn},
  journal={Math. Program.},
  year={1990},
  volume={46},
  pages={255-256}
}
and introduce into basis the nonbasic variable in the pair Yk, zk, with pivot in the kth row. Murty showed in [2] that if M is a P-matrix, then the pivot choice is correct (the pivot is then nonzero due to Tucker 's result [4]) and proved that after a finite number of steps c7 becomes nonnegative and the algorithm terminates with a solution to (1)-(3). We shall reprove here the finiteness of his algorithm using this auxiliary result: