Scaling of symmetric matrices by positive diagonal congruence

DOI10.1080/03081080600872327zbMath1166.15011OpenAlexW2082471948MaRDI QIDQ3615518

Charles R. Johnson, Robert B. Reams

Publication date: 20 March 2009

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

Full work available at URL: https://doi.org/10.1080/03081080600872327

zbMATH Keywords

symmetric matricesstochasticcopositivedoubly stochasticpositive definitediagonal scalingsemipositivetotally scalable

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21) Stochastic matrices (15B51) Conditioning of matrices (15A12)

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Cites Work

• Unnamed Item
• Scalings of matrices which have prespecified row sums and column sums via optimization
• D//\(1AD_ 2 \)theorems for multidimensional matrices
• Matrix scaling: A geometric proof of Sinkhorn's theorem
• Differentiators and the geometry of polynomials.
• A test for copositive matrices
• Spectral theory of copositive matrices
• On the complexity of nonnegative-matrix scaling
• On complexity of matrix scaling
• Concerning nonnegative matrices and doubly stochastic matrices
• Scaling of matrices to achieve specified row and column sums
• 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
• Matrix Analysis
• Some NP-complete problems in quadratic and nonlinear programming
• Diagonal Matrix Scaling and Linear Programming
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
• A Relationship between Arbitrary Positive Matrices and Stochastic Matrices
• Diagonal Equivalence to Matrices with Prescribed Row and Column Sums
• Note on Nonnegative Matrices
• A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents