Matrix scaling: A geometric proof of Sinkhorn's theorem

DOI10.1016/S0024-3795(97)00010-4zbMath0894.15008MaRDI QIDQ1375080

Rafael Cantó, Alberto Borobia

Publication date: 12 August 1998

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

zbMATH Keywords

doubly stochastic matrixpositive matrixmatrix scaling

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Stochastic matrices (15B51) Conditioning of matrices (15A12)

Related Items (2)

Vector Monte Carlo stochastic matrix-based algorithms for large linear systems ⋮ Scaling of symmetric matrices by positive diagonal congruence

Cites Work

• On pairs of multidimensional matrices
• An extension of a theorem of Darroch and Ratcliff in loglinear models and its application to scaling multidimensional matrices
• Matrix scaling, entropy minimization, and conjugate duality. I: Existence conditions
• On the scaling of multidimensional matrices
• Scalings of matrices which have prespecified row sums and column sums via optimization
• Generalized scalings satisfying linear equations
• D//\(1AD_ 2 \)theorems for multidimensional matrices
• Concerning nonnegative matrices and doubly stochastic matrices
• The diagonal equivalence of a nonnegative matrix to a stochastic matrix
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
• Reduction of a Matrix with Positive Elements to a Doubly Stochastic Matrix
• Generalized Iterative Scaling for Log-Linear Models

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