ELA, Volume 6, pp. 11-19, December 1999, abstract. Checking Nonsingularity of Tridiagonal Matrices Ilan Bar-On I. Bar-On, B. Codenotti, and M. Leoncini presented a linear time algorithm for checking the nonsingularity of general tridiagonal matrices [BIT, 36:206, 1996]. A detailed implementation of their algorithm, with some extensions to possibly reducible matrices, is further described in the present paper.