Geodesic
Dual systems of homogeneous linear equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 48-53

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The notion of dual system of homogeneous linear algebraic equations is introduced. A modification of the Gaussian elimination method for the simultaneous solution of primal and dual systems is proposed. An algorithm for solving a homogeneous system of linear equations is validated. The algorithm is based on the technique of the dual representation of the polyhedral cone and, thus, is dual to the known Gauss–Jordan method.
Keywords: dual systems, linear algebraic equations, Gaussian elimination method, dual method, polyhedral cone. 
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     author = {N. N. Astaf'ev},
     title = {Dual systems of homogeneous linear equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {48--53},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a4/}
}
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N. N. Astaf'ev. Dual systems of homogeneous linear equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 48-53. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a4/