On pairs of multidimensional matrices

DOI10.1016/0024-3795(84)90101-0zbMath0567.15010OpenAlexW2048403706MaRDI QIDQ1059694

Thirukkannamangai E. S. Raghavan

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0024-3795(84)90101-0

zbMATH Keywords

Kakutani's fixed point theorempairs of multidimensional matrices

Mathematics Subject Classification ID

Linear programming (90C05) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (12)

An extension of a theorem of Darroch and Ratcliff in loglinear models and its application to scaling multidimensional matrices ⋮ Matrix scaling: A geometric proof of Sinkhorn's theorem ⋮ On the scaling of multidimensional matrices ⋮ Generalized scalings satisfying linear equations ⋮ Unnamed Item ⋮ Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums ⋮ An optimal transport approach for the Schrödinger bridge problem and convergence of Sinkhorn algorithm ⋮ Nonnegative tensors revisited: plane stochastic tensors ⋮ Order independence and factor convergence in iterative scaling ⋮ Better and simpler error analysis of the Sinkhorn-Knopp algorithm for matrix scaling ⋮ Penalized maximum-likelihood estimation, the Baum-Welch algorithm, diagonal balancing of symmetric matrices and applications to training acoustic data ⋮ Iterative Bregman Projections for Regularized Transportation Problems

Cites Work

• Unnamed Item
• D//\(1AD_ 2 \)theorems for multidimensional matrices
• Concerning nonnegative matrices and doubly stochastic matrices
• The spectrum of a nonlinear operator associated with a matrix
• On matrices with doubly stochastic pattern
• The diagonal equivalence of a nonnegative matrix to a stochastic matrix
• The DAD theorem for symmetric non-negative matrices
• Diagonal Equivalence to Matrices with Prescribed Row and Column Sums. II
• The DAD Theorem for Arbitrary Row Sums
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
• Estimating Nonnegative Matrices from Marginal Data
• Reduction of a Matrix with Positive Elements to a Doubly Stochastic Matrix
• Matrix Links, An Extremization Problem, and the Reduction of a Non-Negative Matrix to One With Prescribed Row and Column Sums
• Note on Nonnegative Matrices

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