Geodesic
On a factorization of square matrices with positive determinant
Trudy Instituta matematiki, Tome 25 (2017) no. 1, pp. 51-61

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We prove that any square matrix with positive determinant over the field of real or rational numbers can be represented as a product of nine triangular matrices with positive diagonal elements. This result is the basis for solving of the uniform global attainability problem for linear systems with locally integrable and integrally bounded coefficients. 
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     author = {A. A. Kozlov},
     title = {On a factorization of square matrices with positive determinant},
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A. A. Kozlov. On a factorization of square matrices with positive determinant. Trudy Instituta matematiki, Tome 25 (2017) no. 1, pp. 51-61. http://geodesic.mathdoc.fr/item/TIMB_2017_25_1_a4/