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

Number fields | Densities | Unimodular matrices | MATHEMATICS, APPLIED | PROBABILITY | NATURAL DENSITY | densities | number fields | unimodular matrices

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2014, Volume 459, pp. 264 - 333

The concept of linearization is fundamental for theory, applications, and spectral computations related to matrix polynomials...

Index Sum Theorem | Partial multiplicity sequence | ℓ-ification | Quadratification | Regular | Minimal indices | Companion forms | Unimodular equivalence | Singular | Structured matrix polynomials | Spectral equivalence | Elementary divisors | Matrix pencil | Matrix polynomial | Linearization | Structural indices | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | BASES | EIGENSTRUCTURE | SMITH FORMS | VECTOR-SPACES | MINIMAL INDICES | FULL RANK | MATHEMATICS | RECOVERY | FIEDLER COMPANION LINEARIZATIONS

Index Sum Theorem | Partial multiplicity sequence | ℓ-ification | Quadratification | Regular | Minimal indices | Companion forms | Unimodular equivalence | Singular | Structured matrix polynomials | Spectral equivalence | Elementary divisors | Matrix pencil | Matrix polynomial | Linearization | Structural indices | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | BASES | EIGENSTRUCTURE | SMITH FORMS | VECTOR-SPACES | MINIMAL INDICES | FULL RANK | MATHEMATICS | RECOVERY | FIEDLER COMPANION LINEARIZATIONS

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

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

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

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

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

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

Symmetry, ISSN 2073-8994, 2014, Volume 6, Issue 3, pp. 473 - 515

The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2...

Unimodular matrices | SL(2, c) group | Damped harmonic oscillators | Neutrinos | Gauge invariance | Photons | Poincaré sphere | Sp group | Coupled first-order equations | Wigner's little groups | coupled first-order equations | neutrinos | unimodular | MULTIDISCIPLINARY SCIENCES | photons | NEUTRINO | damped harmonic oscillators | Poincare sphere | matrices | gauge invariance | Damping | Mathematical analysis | Group theory | Poincare spheres | Invariants | Oscillators | Symmetry | Harmonic oscillators | Wigner’s little groups | unimodular matrices

Unimodular matrices | SL(2, c) group | Damped harmonic oscillators | Neutrinos | Gauge invariance | Photons | Poincaré sphere | Sp group | Coupled first-order equations | Wigner's little groups | coupled first-order equations | neutrinos | unimodular | MULTIDISCIPLINARY SCIENCES | photons | NEUTRINO | damped harmonic oscillators | Poincare sphere | matrices | gauge invariance | Damping | Mathematical analysis | Group theory | Poincare spheres | Invariants | Oscillators | Symmetry | Harmonic oscillators | Wigner’s little groups | unimodular matrices

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

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

Two canonical forms for skew-symmetric matrix polynomials over arbitrary fields are characterized...

Minimal symmetric factorization | Unimodular congruence | Skew-symmetric matrix polynomial | Smith form | Smith-McMillan form | Structured linearization | MATHEMATICS, APPLIED | COMPLEX | MINIMAL FACTORIZATIONS | LINEARIZATIONS | MATHEMATICS | HAMILTONIAN SQUARE ROOTS | EIGENVALUES | REAL

Minimal symmetric factorization | Unimodular congruence | Skew-symmetric matrix polynomial | Smith form | Smith-McMillan form | Structured linearization | MATHEMATICS, APPLIED | COMPLEX | MINIMAL FACTORIZATIONS | LINEARIZATIONS | MATHEMATICS | HAMILTONIAN SQUARE ROOTS | EIGENVALUES | REAL

Journal Article

Bulletin of Mathematical Sciences, ISSN 1664-3607, 08/2019, Volume 9, Issue 2, pp. 1950007 - 1950007-68

In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line are studied...

quasi-definite matrix of generalized kernels | VALUED ORTHOGONAL POLYNOMIALS | nondegenerate continuous sesquilinear forms | Matrix biorthogonal polynomials | matrix Geronimus transformations | DETERMINANTS | unimodular matrix polynomials | EQUATIONS | Gauss-Borel factorization | spectral jets | matrix linear spectral transformations | spectral theory of matrix polynomials | MATHEMATICS | quasideterminants | DARBOUX TRANSFORMATIONS | QUASIDETERMINANT SOLUTIONS | Christoffel-type formulas | Gauss–Borel factorization

quasi-definite matrix of generalized kernels | VALUED ORTHOGONAL POLYNOMIALS | nondegenerate continuous sesquilinear forms | Matrix biorthogonal polynomials | matrix Geronimus transformations | DETERMINANTS | unimodular matrix polynomials | EQUATIONS | Gauss-Borel factorization | spectral jets | matrix linear spectral transformations | spectral theory of matrix polynomials | MATHEMATICS | quasideterminants | DARBOUX TRANSFORMATIONS | QUASIDETERMINANT SOLUTIONS | Christoffel-type formulas | Gauss–Borel factorization

Journal Article

Multidimensional Systems and Signal Processing, ISSN 0923-6082, 4/2015, Volume 26, Issue 2, pp. 503 - 517

The paper proposes a two step algorithm that reduces a bivariate polynomial matrix $$T\left( s,z\right...

Secondary: 93B17 | Zero coprime equivalence | Signal, Image and Speech Processing | Companion form | Primary: 93B18 | Bivariate polynomial matrix | Unimodular equivalence | Newton basis | Lagrange basis | 93B25 | 93C35 | Engineering | 93B11 | 93C05 | Artificial Intelligence (incl. Robotics) | Matrix pencil | Circuits and Systems | Electrical Engineering | 93B40 | LINEAR-SYSTEMS | 2-D SYSTEMS | PENCIL EQUIVALENTS | ENGINEERING, ELECTRICAL & ELECTRONIC | REDUCTION | STATE-SPACE REALIZATIONS | POLES | COMPUTER SCIENCE, THEORY & METHODS | TRANSFORMATIONS | ZEROS | Algorithms

Secondary: 93B17 | Zero coprime equivalence | Signal, Image and Speech Processing | Companion form | Primary: 93B18 | Bivariate polynomial matrix | Unimodular equivalence | Newton basis | Lagrange basis | 93B25 | 93C35 | Engineering | 93B11 | 93C05 | Artificial Intelligence (incl. Robotics) | Matrix pencil | Circuits and Systems | Electrical Engineering | 93B40 | LINEAR-SYSTEMS | 2-D SYSTEMS | PENCIL EQUIVALENTS | ENGINEERING, ELECTRICAL & ELECTRONIC | REDUCTION | STATE-SPACE REALIZATIONS | POLES | COMPUTER SCIENCE, THEORY & METHODS | TRANSFORMATIONS | ZEROS | Algorithms

Journal Article

Bulletin of Mathematical Sciences, ISSN 1664-3607, 2018

Spectral theory of matrix polynomials | Christoffel type formulas | Matrix biorthogonal polynomials | Unimodular matrix polynomials | Matrix linear spectral transformations | Quasideterminants | Gauss–Borel factorization | Quasidefinite matrix of generalized kernels | Matrix Geronimus transformations | Nondegenerate continuous sesquilinear forms | Spectral jets

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

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

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

In this paper, we study matrix valued positive definite functions on a unimodular group...

43A35 | Unimodular group | Moderated functions | 43A15 | 22D | Positive definite function | Square integrable functions | Mathematics, general | Mathematics | Convolution algebra | Unitary representations | MATHEMATICS | CLASSICAL-GROUPS | THETA-CORRESPONDENCE | Algebra

43A35 | Unimodular group | Moderated functions | 43A15 | 22D | Positive definite function | Square integrable functions | Mathematics, general | Mathematics | Convolution algebra | Unitary representations | MATHEMATICS | CLASSICAL-GROUPS | THETA-CORRESPONDENCE | Algebra

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2013, Volume 244, Issue 1, pp. 49 - 66

Polyphase matrix extension of multiscaling vectors is a fundamental approach for the construction of compactly supported biorthogonal multiwavelets...

Compactly supported biorthogonal multiwavelets | Unimodular square matrix | Group action | Symmetric extension of polyphase matrices | Explicit formulas | MATHEMATICS, APPLIED | ALGORITHM | MATRIX EXTENSION | WAVELETS | Construction | Mathematical analysis | Canonical forms | Mathematical models | Matrices | Vectors (mathematics) | Matrix methods | Rings (mathematics)

Compactly supported biorthogonal multiwavelets | Unimodular square matrix | Group action | Symmetric extension of polyphase matrices | Explicit formulas | MATHEMATICS, APPLIED | ALGORITHM | MATRIX EXTENSION | WAVELETS | Construction | Mathematical analysis | Canonical forms | Mathematical models | Matrices | Vectors (mathematics) | Matrix methods | Rings (mathematics)

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

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

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

MATHEMATICS | UNIMODULAR MATRICES | MATROIDS | GRAPHS

Journal Article

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