O. H. Ibarra, S. Moran, and R. Hui, A generalization of the fast LUP matrix decomposition algorithm and applications, Journal of Algorithms, vol.3, issue.1, pp.45-56, 1982.
DOI : 10.1016/0196-6774(82)90007-4

D. J. Jeffrey, LU factoring of non-invertible matrices, ACM SIGSAM Bulletin, vol.44, issue.1/2
DOI : 10.1145/1838599.1838602

J. Dumas, P. Giorgi, and C. Pernet, Dense Linear Algebra over Word-Size Prime Fields, ACM Transactions on Mathematical Software, vol.35, issue.3, pp.1-42, 2008.
DOI : 10.1145/1391989.1391992

URL : https://hal.archives-ouvertes.fr/hal-00018223

C. Jeannerod, C. Pernet, and A. Storjohann, Rank-profile revealing Gaussian elimination and the CUP matrix decomposition, Journal of Symbolic Computation, vol.56, 2013.
DOI : 10.1016/j.jsc.2013.04.004

URL : https://hal.archives-ouvertes.fr/hal-00655543

A. Storjohann and . Eth-zentrum, Algorithms for matrix canonical forms, pp.10-3929, 2000.

K. Klimkowski and R. A. Van-de-geijn, Anatomy of a parallel out-of-core dense linear solver, International Conference on Parallel Processing, pp.29-33, 1995.

J. Dumas, C. Pernet, and Z. Sultan, Recursion based parallelization of exact dense linear algebra routines for Gaussian elimination, Parallel Computing, vol.57
DOI : 10.1016/j.parco.2015.10.003

URL : https://hal.archives-ouvertes.fr/hal-01084238

J. Dumas, C. Pernet, and Z. Sultan, Simultaneous computation of the row and column rank profiles, Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation, ISSAC '13, pp.181-188, 2013.
DOI : 10.1145/2465506.2465517

URL : https://hal.archives-ouvertes.fr/hal-00778136

J. Dumas, C. Pernet, and Z. Sultan, Computing the Rank Profile Matrix, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pp.149-156
DOI : 10.1145/2755996.2756682

URL : https://hal.archives-ouvertes.fr/hal-01107722

F. Bruhat, Sur les repr??sentations induites des groupes de Lie, Bulletin de la Société mathématique de France, vol.79, pp.97-205, 1956.
DOI : 10.24033/bsmf.1469

J. and D. Dora, Sur quelques algorithmes de recherche de valeurs propres, Theses, 1973.

D. Y. Grigor-'ev, Analogy of Bruhat decomposition for the closure of a cone of Chevalley group of a classical serie, Soviet Mathematics Doklady, vol.23, issue.2, pp.393-397, 1981.

N. Bourbaki, Groupes et Algègres de Lie, no. Chapters 4?6 in Elements of mathematics, 2008.

G. I. Malaschonok, Fast Generalized Bruhat Decomposition, CASC'10, pp.194-202, 2010.
DOI : 10.1090/S0025-5718-1974-0331751-8

W. Manthey and U. Helmke, Bruhat canonical form for linear systems, Linear Algebra and its Applications, vol.425, issue.2-3, pp.261-282, 2007.
DOI : 10.1016/j.laa.2007.01.022

H. Y. Cheung, T. C. Kwok, and L. C. Lau, Fast matrix rank algorithms and applications, Journal of the ACM, vol.60, issue.5, pp.1-31, 2013.
DOI : 10.1145/2528404

A. Storjohann and S. Yang, Linear independence oracles and applications to rectangular and low rank linear systems, Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ISSAC '14, pp.381-388
DOI : 10.1145/2608628.2608673

E. Tyrtyshnikov, Matrix Bruhat decompositions with a remark on the QR (GR) algorithm, Linear Algebra and its Applications, vol.250, issue.95, pp.61-68, 1997.
DOI : 10.1016/0024-3795(95)00453-X

N. H. Mccoy, Rings and ideals, Carus Monograph Series, 1948.

J. Dumas, B. D. Saunders, and G. Villard, On Efficient Sparse Integer Matrix Smith Normal Form Computations, Journal of Symbolic Computation, vol.32, issue.1-2, pp.71-99, 2001.
DOI : 10.1006/jsco.2001.0451

W. C. Brown, Null ideals and spanning ranks of matrices, Communications in Algebra, vol.1, issue.2, pp.2401-2417, 1998.
DOI : 10.1080/00927879808826285

W. Keller-gehrig, Fast algorithms for the characteristics polynomial, Theoretical Computer Science, vol.36, pp.309-317, 1985.
DOI : 10.1016/0304-3975(85)90049-0

J. Dumas and J. Roch, On parallel block algorithms for exact triangularizations, Parallel Computing, vol.28, issue.11, pp.1531-154810, 2002.
DOI : 10.1016/S0167-8191(02)00161-8

J. Dumas, T. Gautier, C. Pernet, and Z. , Sultan, Parallel computation of echelon forms, Euro-Par 2014 Parallel Proc, pp.499-510, 2014.

G. Malaschonok, Generalized Bruhat Decomposition in Commutative Domains, Computer Algebra in Scientific Computing Lecture Notes in Computer Science, vol.8136, pp.231-242, 2013.
DOI : 10.1007/978-3-319-02297-0_20

E. Kaltofen and B. D. Saunders, On Wiedemann's method of solving sparse linear systems Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, no, Lecture Notes in Computer Science, issue.539, pp.29-38, 1991.

P. V. Strassen, Gaussian elimination is not optimal, Numerische Mathematik, vol.13, issue.4, pp.354-356, 1969.
DOI : 10.1007/BF02165411