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SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2019, Volume 33, Issue 1, pp. 425 - 437
Let n and m be positive integers such that n < m. In this paper we compute the density of rectangular unimodular n x m matrices over the ring of algebraic... 
Number fields | Densities | Unimodular matrices | MATHEMATICS, APPLIED | PROBABILITY | NATURAL DENSITY | densities | number fields | unimodular matrices
Journal Article
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 2020, Volume 586, pp. 377 - 409
Let Tn(q) be the ring of lower triangular matrices of order n≥2 with entries from the finite field F(q) of order q≥2 and let Tn2(q... 
Projective ring lines | Non-unimodular free cyclic submodules | Rings of lower triangular matrices | Affine | Projective planes | MATHEMATICS | MATHEMATICS, APPLIED | Planes | Fields (mathematics) | Rings (mathematics) | Mathematics - Rings and Algebras
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2014, Volume 444, pp. 219 - 226
In this paper, some connections of dense alternating sign matrices with total unimodularity, combined matrices, and generalized complementary basic matrices... 
Dense matrix | Totally unimodular matrix | Alternating sign matrix | Combined matrix | Generalized complementary basic matrix | COMPLEMENTARY BASIC MATRICES | MATHEMATICS, APPLIED | Computer science
Journal Article
Optimization Letters, ISSN 1862-4472, 2/2017, Volume 11, Issue 2, pp. 407 - 418
Networks are frequently studied algebraically through matrices. In this work, we show that networks may be studied in a more abstract level using results... 
Computational Intelligence | Complex networks | Matroids | Mathematics | Operation Research/Decision Theory | Numerical and Computational Physics, Simulation | Totally unimodular matrices | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2013, Volume 438, Issue 6, pp. 2675 - 2682
In this note, we show that the probability that a uniformly random k×n matrix over Fq[x] can be extended to an n... 
Finite field | Polynomial ring | Unimodular matrices | Riemann’s zeta function | q-Zeta function | Natural density | Riemann's zeta function
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2011, Volume 434, Issue 5, pp. 1319 - 1324
In this paper, we compute the natural density of the set of k×n integer matrices that can be extended to an invertible n... 
Quillen–Suslin’s Theorem | Unimodular matrices | Cesàro’s Theorem | Natural density | Cesàro's Theorem | Quillen-Suslin's Theorem | Cesaro's Theorem | MATHEMATICS, APPLIED | PROBABILITY | COMPLETION
Journal Article
Optimization Letters, ISSN 1862-4472, 8/2016, Volume 10, Issue 6, pp. 1179 - 1189
In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded... 
Integer programming | Polytope | Matrix minors | Computational Intelligence | Unimodular decomposition | Flatness theorem | Efficient algorithm | Numerical and Computational Physics | Mathematics | Operation Research/Decision Theory | Width | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EMPTY LATTICE SIMPLICES | NONSYMMETRIC CONVEX-BODIES | GRAPHS | Algorithms
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 06/2013, Volume 438, Issue 12, pp. 4625 - 4653
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 05/2012, Volume 33, Issue 4, pp. 519 - 533
It has been observed by Assmus and Key as a result of the complete classification of Hadamard matrices of order 24, that the extremality of the binary code of a Hadamard matrix H of order 24... 
MATHEMATICS | II CODES | SELF-DUAL CODES | UNIMODULAR LATTICES | Mathematical analysis | Lattices | Binary codes | Classification | Proving | Matrices | Matrix methods | Combinatorial analysis | Mathematics - Combinatorics
Journal Article
Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2018, Volume 55, Issue 1, pp. 41 - 50
This paper mainly considers a tuple of multiplication operators on Bergman spaces over polydisks which essentially arise from a matrix, their joint reducing subspaces and associated von Neumann algebras... 
Joint reducing subspace | Von Neumann algebra | Unimodular matrix | ANALYTIC TOEPLITZ OPERATOR | BIDISK | MATHEMATICS | joint reducing subspace | COMMUTANT | von Neumann algebra | REDUCING SUBSPACES | unimodular matrix
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 7/2015, Volume 177, Issue 3, pp. 437 - 449
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2013, Volume 244, Issue 1, pp. 49 - 66
Journal Article
Control and Cybernetics, ISSN 0324-8569, 2013, Volume 42, Issue 2, pp. 543 - 551
...1. Introduction In the polynomial approach, pioneered by Rosenbrock (1970), matrices over R[s], s [equivalent to] d/dt are used to represent linear systems... 
Gröbner bases | Multivariate polynomial matrices | Smith form | Linear functional systems | Unimodular equivalence
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 04/2016, Volume 495, pp. 1 - 10
Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field... 
Reachable pair | Zero kernel pair | Finite field | Unimodular matrix polynomial | Observable pair | Matrix completion | MATHEMATICS | MATHEMATICS, APPLIED | MATRICES | Mathematics - Combinatorics
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 11/1999, Volume 77, Issue 2, pp. 292 - 406
A 0, 1 matrix is balanced if it does not contain a square submatrix of odd order with two ones per row and per column... 
MATHEMATICS | UNIMODULAR MATRICES | MATROIDS | GRAPHS
Journal Article
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