The role of pivoting in proving some fundamental theorems of linear algebra

DOI10.1016/0024-3795(91)90356-2zbMath0724.15005OpenAlexW1964825436MaRDI QIDQ2644727

Emil Klafszky, Tamás Terlaky

Publication date: 1991

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(91)90356-2

zbMATH Keywords

Kronecker-Capelli theoremFarkas theoremmatrix rank theoremmethod of pivoting

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Miscellaneous inequalities involving matrices (15A45) Vector spaces, linear dependence, rank, lineability (15A03) Linear equations (linear algebraic aspects) (15A06)

Related Items

New variants of the criss-cross method for linearly constrained convex quadratic programming ⋮ The \(s\)-monotone index selection rules for pivot algorithms of linear programming ⋮ Exterior point simplex-type algorithms for linear and network optimization problems ⋮ Computational aspects of simplex and MBU-simplex algorithms using different anti-cycling pivot rules ⋮ The s-monotone index selection rule for criss-cross algorithms of linear complementarity problems ⋮ Finiteness of the quadratic primal simplex method when \(\mathbf s\)-monotone index selection rules are applied ⋮ The finite criss-cross method for hyperbolic programming ⋮ New criss-cross type algorithms for linear complementarity problems with sufficient matrices ⋮ New variants of finite criss-cross pivot algorithms for linear programming

Cites Work

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• An exponential example for Terlaky's pivoting rule for the criss-cross simplex method
• A finite crisscross method for oriented matroids
• The Criss-Cross Method for Solving Linear Programming Problems
• A convergent criss-cross method
• New Finite Pivoting Rules for the Simplex Method
• THE STRONG MINKOWSKI FARKAS-WEYL THEOREM FOR VECTOR SPACES OVER ORDERED FIELDS
• Duality Theory of Linear Programs: A Constructive Approach with Applications

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