Gérald Bourgeois

Vice Président de la SMF

Research interests

Cryptography. Linear algebra and symbolic computation. Symbolic computation applied to geometry.

Recent Publications

• G. Bourgeois: Nonsymmetric generic matrix equations, Accepted in Linear Algebra and its Applications (2014).
• G. Bourgeois: The Matrix Equation XA-AX=X^alpha g(X) over Fields or Rings, Hindawi Algebra, Vol. 2014 (2014), Article ID 745029.
• G. Bourgeois: About the matrix function X->AX+XA, Linear and Multilinear Algebra, Vol. 62-7 (2014) p. 978-987 and Corrigendum: Vol. 62-8 (2014) p. 1137.
• G. Bourgeois: Property L and commuting exponentials in dimension at most three. Bulletin of the Australian Mathematical Society, volume 89, numéro 1, pages 70-78, 2014.
• G. Bourgeois: Common invariant subspace and commuting matrices. Linear Algebra and its applications, volume 438, numéro 7, pages 3030-3038, 2013.
• G. Bourgeois: Similar powers of a matrix. Linear and Multilinear Algebra, volume 61, numéro 6, pages 699-709, 2013.
• G. Bourgeois, S. Orange: Dynamical systems of simplices in dimension 2 or 3. Dans : Automated Deduction in Geometry - ADG 2008, Springer, Lecture Notes in Computer Science, volume 6301, pages 1-21, 2011.
• G. Bourgeois: How to solve the equation XA-AX = f(X). Linear Algebra and its Applications, volume 434, pages 657-668, 2011.
• G. Bourgeois: Pairs of matrices, one of which commutes with their commutator. Electronic Journal of Linear Algebra, volume 22, pages 593-597, 2011.
• G. Bourgeois: The matrix equation, log(XY)=log(X)+log(Y). Linear Algebra and its Applications, volume 432, pages 1878-1884, 2010.
• G. Bourgeois, Jean-Charles Faugère: Algebraic attack on NTRU using Witt vectors and Gröbner bases. Journal of Mathematical Cryptology, volume 3, pages 205-214, 2009.
• G. Bourgeois: Algebraic system theory and Gröbner basis theory. Linear Algebra and its Applications, volume 430, numéro 8-9, pages 2157-2169, 2009.
• G. Bourgeois: On commuting exponentials in low dimensions. Linear Algebra and its Applications, volume 423, numéro 2-3, pages 277-286, 2007.