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The completely positive maps, a generalization of the nonnegative matrices, are a well-studied class of maps from $n\times n$ matrices to $m\times m$ matrices.
Doubly stochastic matrices and the diagonal of a rotation matrix
Alfred Horn · 1954
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Eigenvalues of sums of hermitian matrices
Alfred Horn · 1962
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A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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Submodular functions, matroids, and certain polyhedra
Jack Edmonds · 1970
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An effective method of investigation of positive maps on the set of positive definite operators
A Jamiołkowski · 1974
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Sur l’image de l’application moment
Michel Brion · 1987
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Scalings of matrices which have prespecified row sums and column sums via optimization
Uriel G Rothblum and Hans Schneider · 1989
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On a reverse form of the brascamp-lieb inequality
Franck Barthe · 1998
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Stable bundles, representation theory and hermitian operators
Alexander A Klyachko · 1998
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A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
Nathan Linial, Alex Samorodnitsky, and Avi Wigderson · 1998
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The red book of varieties and schemes, second, expanded edition, volume 1358 of lnm, 1999
D Mumford · 1999
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Eigenvalues, invariant factors, highest weights, and schubert calculus
William Fulton · 2000
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Allen Knutson and Terence Tao · 2000
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A linear lower bound on the unbounded error probabilistic communication complexity
Jürgen Forster · 2002
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Moment polytopes of projective g-varieties and tensor products of symmetric group representations
Matthias Franz · 2002
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Classical complexity and quantum entanglement
Leonid Gurvits · 2004
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Introductory schubert calculus
Veerle Ledoux and Simon JA Malham · 2010
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On schrodinger’s bridge problem
Shmuel Friedland · 2016
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Algorithmic aspects of brascamp-lieb inequalities
Ankit Garg, Leonid Gurvits, Rafael Oliveira, and Avi Wigderson · 2016
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A deterministic polynomial time algorithm for non-commutative rational identity testing
Ankit Garg, Leonid Gurvits, Rafael Oliveira, and Avi Wigderson · 2016
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Much faster algorithms for matrix scaling
Zeyuan Allen-Zhu, Yuanzhi Li, Rafael Oliveira, and Avi Wigderson · 2017
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Membership in moment polytopes is in NP and coNP
Peter Bürgisser, Matthias Christandl, Ketan D Mulmuley, and Michael Walter · 2017
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Algebraic geometry (v6.02), 2017
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