IEEE Transactions on Automatic Control, ISSN 0018-9286, 08/2019, Volume 64, Issue 8, pp. 3085 - 3100

Within the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of Sarymsakov matrices is the largest known subset that is closed under...

products of stochastic matrices | Symmetric matrices | multi-agent systems | Stochastic processes | Cooperative control | doubly stochastic matrices | Sarymsakov matrices | Robot sensing systems | Linear matrix inequalities | Indexes | Standards | Convergence | ERGODICITY | MULTIAGENT SYSTEMS | COORDINATION | NETWORKS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | DYNAMICALLY CHANGING ENVIRONMENT | CONVERGENCE SPEED | OPTIMIZATION | CONSENSUS SEEKING | DISTRIBUTED CONSENSUS | AUTOMATION & CONTROL SYSTEMS

products of stochastic matrices | Symmetric matrices | multi-agent systems | Stochastic processes | Cooperative control | doubly stochastic matrices | Sarymsakov matrices | Robot sensing systems | Linear matrix inequalities | Indexes | Standards | Convergence | ERGODICITY | MULTIAGENT SYSTEMS | COORDINATION | NETWORKS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | DYNAMICALLY CHANGING ENVIRONMENT | CONVERGENCE SPEED | OPTIMIZATION | CONSENSUS SEEKING | DISTRIBUTED CONSENSUS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 3/2017, Volume 27, Issue 1, pp. 475 - 489

The Jordan forms of matrices that are the product of two skew-symmetric matrices over a field of characteristic $${\neq 2}$$ ≠ 2 have been a research topic in...

{SL(4,\mathbb{R})}$$ S L ( 4 , R ) | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Line geometry | Product of two skew-symmetric matrices | Applications of Mathematics | Physics, general | Primary 15B99 | Physics | Secondary 51J10 | Oriented projective geometry | {SL(4,\mathbb{R})}$$ S L ( 4 , R ) -Jordan form | SL(4 , R) | SL(4 , R) -Jordan form | MATHEMATICS, APPLIED | SL(4, R)-Jordan form | PHYSICS, MATHEMATICAL | SL(4, R)

{SL(4,\mathbb{R})}$$ S L ( 4 , R ) | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Line geometry | Product of two skew-symmetric matrices | Applications of Mathematics | Physics, general | Primary 15B99 | Physics | Secondary 51J10 | Oriented projective geometry | {SL(4,\mathbb{R})}$$ S L ( 4 , R ) -Jordan form | SL(4 , R) | SL(4 , R) -Jordan form | MATHEMATICS, APPLIED | SL(4, R)-Jordan form | PHYSICS, MATHEMATICAL | SL(4, R)

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 418, Issue 2, pp. 939 - 954

A direct method, based on the projection theorem in inner products spaces, the generalized singular value decomposition and the canonical correlation...

Canonical correlation decomposition | Symmetric matrix | Generalized singular value decomposition | Least-squares solution | Optimal approximate solution | canonical correlation decomposition | symmetric matrix | MATHEMATICS, APPLIED | A1XB1=C1 | optimal approximate solution | IMPROVEMENT | generalized singular value decomposition | A2XB2=C2 | least-squares solution | SINGULAR VALUE DECOMPOSITION | PAIR | Yuan (China) | Algorithms

Canonical correlation decomposition | Symmetric matrix | Generalized singular value decomposition | Least-squares solution | Optimal approximate solution | canonical correlation decomposition | symmetric matrix | MATHEMATICS, APPLIED | A1XB1=C1 | optimal approximate solution | IMPROVEMENT | generalized singular value decomposition | A2XB2=C2 | least-squares solution | SINGULAR VALUE DECOMPOSITION | PAIR | Yuan (China) | Algorithms

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2018, Volume 64, Issue 4, pp. 3179 - 3196

We consider the problem of generating symmetric pseudo-random sign (±1) matrices based on the similarity of their spectra to Wigner's semicircular law. Using...

Symmetric matrices | Limiting | Wigner ensemble | Signal processing algorithms | semicircular law | Complexity theory | Pseudo-random matrices | Covariance matrices | Physics | Convergence | UNIVERSALITY | SEQUENCES | ENSEMBLES | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC CODES | ARRAYS | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | WIGNER RANDOM MATRICES | PERFECT MAPS | COVARIANCE MATRICES | Mathematical analysis | Matrix methods

Symmetric matrices | Limiting | Wigner ensemble | Signal processing algorithms | semicircular law | Complexity theory | Pseudo-random matrices | Covariance matrices | Physics | Convergence | UNIVERSALITY | SEQUENCES | ENSEMBLES | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC CODES | ARRAYS | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | WIGNER RANDOM MATRICES | PERFECT MAPS | COVARIANCE MATRICES | Mathematical analysis | Matrix methods

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2018, Volume 64, Issue 4, pp. 3170 - 3178

We consider the problem of generating pseudo-random matrices based on the similarity of their spectra to Wigner's semicircular law. We introduce the notion of...

Symmetric matrices | Wigner ensemble | Signal processing algorithms | Linear codes | semicircular law | Complexity theory | Random variables | Power capacitors | Pseudo-random matrices | Convergence | EIGENVALUES | LAW | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC CODES | ARRAYS | PERFECT MAPS | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer simulation | Graphs | BCH codes

Symmetric matrices | Wigner ensemble | Signal processing algorithms | Linear codes | semicircular law | Complexity theory | Random variables | Power capacitors | Pseudo-random matrices | Convergence | EIGENVALUES | LAW | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC CODES | ARRAYS | PERFECT MAPS | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer simulation | Graphs | BCH codes

Journal Article

Journal of Combinatorial Designs, ISSN 1063-8539, 11/2017, Volume 25, Issue 11, pp. 507 - 522

We show that the existence of {±1}‐matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular,...

D‐optimal design | EW matrix | conference matrix | skew‐symmetric matrix | D-optimal design | skew-symmetric matrix | MATHEMATICS | MATRICES | Mathematics - Combinatorics

D‐optimal design | EW matrix | conference matrix | skew‐symmetric matrix | D-optimal design | skew-symmetric matrix | MATHEMATICS | MATRICES | Mathematics - Combinatorics

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 2013, Volume 2013, pp. 1 - 15

The matrix equation Sigma(u)(l=1) A(i)XB(i) + Sigma(v)(s=1) (CsXDs)-D-T = F, which includes some frequently investigated matrix equations as its special cases,...

MATHEMATICS | MATHEMATICS, APPLIED | OPTIMAL APPROXIMATION SOLUTION | SINGULAR-VALUE DECOMPOSITION | REFLEXIVE MATRICES | MINIMUM-NORM | COMMON SOLUTION | SYSTEMS | SYMMETRIC-SOLUTIONS | AXB | LEAST-SQUARES SOLUTION | BIDIAGONALIZATION | Matrices | Algorithms | Research | Mathematical research | Iterative methods (Mathematics)

MATHEMATICS | MATHEMATICS, APPLIED | OPTIMAL APPROXIMATION SOLUTION | SINGULAR-VALUE DECOMPOSITION | REFLEXIVE MATRICES | MINIMUM-NORM | COMMON SOLUTION | SYSTEMS | SYMMETRIC-SOLUTIONS | AXB | LEAST-SQUARES SOLUTION | BIDIAGONALIZATION | Matrices | Algorithms | Research | Mathematical research | Iterative methods (Mathematics)

Journal Article

1973, Prentice-Hall series in automatic computation., ISBN 0136265561, xi, 276

Book

IEEE Transactions on Signal Processing, ISSN 1053-587X, 11/2014, Volume 62, Issue 22, pp. 6059 - 6070

In this paper, a general class of regularized M-estimators of scatter matrix are proposed that are suitable also for low or insufficient sample support (small...

Maximum likelihood estimation | Symmetric matrices | regularization | robustness | Covariance matrices | Equations | Geodesic convexity | complex elliptically symmetric distributions | M -estimator of scatter | Cost function | normalized matched filter | Convex functions | High definition video | M$-estimator of scatter | M-estimator of scatter | CONVEXITY | SUBSPACE DETECTORS | MULTIVARIATE LOCATION | ENGINEERING, ELECTRICAL & ELECTRONIC | CFAR DETECTION | COVARIANCE-MATRIX | MODELS | GAUSSIAN DISTRIBUTION | Signal processing | Usage | Mathematical optimization | Iterative methods (Mathematics) | Least squares | Innovations | Mathematical analysis | Radar detection | Uniqueness | Exact solutions | Transaction processing | Scatter | Estimators | Convergence

Maximum likelihood estimation | Symmetric matrices | regularization | robustness | Covariance matrices | Equations | Geodesic convexity | complex elliptically symmetric distributions | M -estimator of scatter | Cost function | normalized matched filter | Convex functions | High definition video | M$-estimator of scatter | M-estimator of scatter | CONVEXITY | SUBSPACE DETECTORS | MULTIVARIATE LOCATION | ENGINEERING, ELECTRICAL & ELECTRONIC | CFAR DETECTION | COVARIANCE-MATRIX | MODELS | GAUSSIAN DISTRIBUTION | Signal processing | Usage | Mathematical optimization | Iterative methods (Mathematics) | Least squares | Innovations | Mathematical analysis | Radar detection | Uniqueness | Exact solutions | Transaction processing | Scatter | Estimators | Convergence

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2018, Volume 555, pp. 84 - 91

A square matrix is called diagonally singularizable if holds for some singular matrix ( is the identity matrix). The paper brings several necessary and/or...

Singularity | Symmetric alternative | Diagonal singularizability | Preservation | Square matrix | MATHEMATICS | MATHEMATICS, APPLIED

Singularity | Symmetric alternative | Diagonal singularizability | Preservation | Square matrix | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2010, Volume 432, Issue 6, pp. 1531 - 1552

In the present paper, by extending the idea of conjugate gradient (CG) method, we construct an iterative method to solve the general coupled matrix equations...

Generalized bisymmetric matrix | Least Frobenius norm solution group | Iterative method | General coupled matrix equations | Optimal approximation generalized bisymmetric solution group | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | bisymmetric solution group | SYLVESTER EQUATIONS | REGULAR-RINGS | EFFICIENT ITERATIVE METHOD | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | IDENTIFICATION | General Coupled matrix equations | REFLEXIVE SOLUTIONS | Optimal approximation generalized | SYSTEMS

Generalized bisymmetric matrix | Least Frobenius norm solution group | Iterative method | General coupled matrix equations | Optimal approximation generalized bisymmetric solution group | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | bisymmetric solution group | SYLVESTER EQUATIONS | REGULAR-RINGS | EFFICIENT ITERATIVE METHOD | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | IDENTIFICATION | General Coupled matrix equations | REFLEXIVE SOLUTIONS | Optimal approximation generalized | SYSTEMS

Journal Article

04/2016, 2nd ed. 2016, ISBN 1493934066, 501

eBook

IEEE Transactions on Signal Processing, ISSN 1053-587X, 04/2011, Volume 59, Issue 4, pp. 1409 - 1420

The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to...

Target tracking | Symmetric matrices | group targets | Bayesian methods | formations | random matrices | Measurement uncertainty | sensor resolution | Kinematics | Extended targets | Approximation methods | Equations | target tracking | MAINTENANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Bayesian statistical decision theory | Random matrices | Usage | Innovations | Signal processing | Sensors | Methods | Bayesian analysis | Object extensions | Tasks | Tracking | Mathematical analysis | Error detection | Spreads | Maintenance

Target tracking | Symmetric matrices | group targets | Bayesian methods | formations | random matrices | Measurement uncertainty | sensor resolution | Kinematics | Extended targets | Approximation methods | Equations | target tracking | MAINTENANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Bayesian statistical decision theory | Random matrices | Usage | Innovations | Signal processing | Sensors | Methods | Bayesian analysis | Object extensions | Tasks | Tracking | Mathematical analysis | Error detection | Spreads | Maintenance

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2019, Volume 577, pp. 114 - 120

The purpose of this paper is to evaluate the Pfaffians of certain Toeplitz payoff matrices associated with integer choice matrix games.

Payoff matrix | Toeplitz skew-symmetric matrix | Matrix game | Pfaffian | Nullity | MATHEMATICS | MATHEMATICS, APPLIED

Payoff matrix | Toeplitz skew-symmetric matrix | Matrix game | Pfaffian | Nullity | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Acta Mathematica, ISSN 0001-5962, 3/2011, Volume 206, Issue 1, pp. 127 - 204

In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined...

15A52 | Mathematics, general | Mathematics | POLYNOMIALS | MATHEMATICS | WIGNER RANDOM MATRICES | ENSEMBLES | DELOCALIZATION | SEMICIRCLE LAW | SYMMETRIC-MATRICES | CONVERGENCE | BULK UNIVERSALITY | ASYMPTOTICS | SPECTRUM | Eigenvalues | Correlation | Matrices | Mathematical analysis | Matrix methods | Statistics

15A52 | Mathematics, general | Mathematics | POLYNOMIALS | MATHEMATICS | WIGNER RANDOM MATRICES | ENSEMBLES | DELOCALIZATION | SEMICIRCLE LAW | SYMMETRIC-MATRICES | CONVERGENCE | BULK UNIVERSALITY | ASYMPTOTICS | SPECTRUM | Eigenvalues | Correlation | Matrices | Mathematical analysis | Matrix methods | Statistics

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 11/2011, Volume 59, Issue 11, pp. 5338 - 5352

In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear...

multiple-input multiple-output (MIMO) radar | direction of arrival (DOA) estimation | Symmetric matrices | Compressive sensing | MIMO radar | Transmitting antennas | Receiving antennas | Coherence | measurement matrix | Sensors | Sparse matrices | SIGNAL RECOVERY | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Random noise theory | Simulation methods | Innovations | MIMO communications | Studies | Radar | Waveforms | Gaussian | Matrices | Criteria | Detection | Position (location) | Optimization

multiple-input multiple-output (MIMO) radar | direction of arrival (DOA) estimation | Symmetric matrices | Compressive sensing | MIMO radar | Transmitting antennas | Receiving antennas | Coherence | measurement matrix | Sensors | Sparse matrices | SIGNAL RECOVERY | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Random noise theory | Simulation methods | Innovations | MIMO communications | Studies | Radar | Waveforms | Gaussian | Matrices | Criteria | Detection | Position (location) | Optimization

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 03/2009, Volume 57, Issue 3, pp. 878 - 891

We propose a new low-complexity approximate joint diagonalization (AJD) algorithm, which incorporates nontrivial block-diagonal weight matrices into a weighted...

auto regressive processes | Source separation | Symmetric matrices | Predictive models | Biomedical computing | Blind source separation | Covariance matrix | blind source separation (BSS) | Signal processing algorithms | Approximate joint diagonalization (AJD) | Iterative algorithms | Large-scale systems | nonstationary random processes | Autoregressive processes | Nonstationary random processes | Auto regressive processes | Blind source separation (BSS) | 2ND-ORDER STATISTICS | MIXTURE | BLIND SOURCE SEPARATION | GAUSSIAN SOURCES | ADDITIVE NOISE | ALGORITHMS | auto-regressive processes | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Asymptotes | Stochastic processes | Analysis | Autoregression (Statistics) | Signal processing | Research | Studies | Algorithms | Approximation | Asymptotic properties | Mathematical analysis | Blocking | Matrices | Matrix methods | Optimization

auto regressive processes | Source separation | Symmetric matrices | Predictive models | Biomedical computing | Blind source separation | Covariance matrix | blind source separation (BSS) | Signal processing algorithms | Approximate joint diagonalization (AJD) | Iterative algorithms | Large-scale systems | nonstationary random processes | Autoregressive processes | Nonstationary random processes | Auto regressive processes | Blind source separation (BSS) | 2ND-ORDER STATISTICS | MIXTURE | BLIND SOURCE SEPARATION | GAUSSIAN SOURCES | ADDITIVE NOISE | ALGORITHMS | auto-regressive processes | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Asymptotes | Stochastic processes | Analysis | Autoregression (Statistics) | Signal processing | Research | Studies | Algorithms | Approximation | Asymptotic properties | Mathematical analysis | Blocking | Matrices | Matrix methods | Optimization

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2017, Volume 530, pp. 160 - 184

In this paper we study the minimal matrices for the Bruhat order on the class of symmetric -matrices with given row sum vector. We will show that, when...

Term rank | Symmetric matrices | Minimal matrices | [formula omitted]-matrices | Bruhat order | (0,1)-matrices | MATHEMATICS | MATHEMATICS, APPLIED | ROW

Term rank | Symmetric matrices | Minimal matrices | [formula omitted]-matrices | Bruhat order | (0,1)-matrices | MATHEMATICS | MATHEMATICS, APPLIED | ROW

Journal Article

Signal Processing, ISSN 0165-1684, 12/2019, Volume 165, pp. 163 - 174

Covariance matrix estimation is a ubiquitous problem in signal processing. In most modern signal processing applications, data are generally modeled by...

Scatter matrix estimation | Structured covariance matrix | Complex elliptically symmetric distributions | Mismatched framework | BOUNDS | CALCULUS | MULTIVARIATE LOCATION | KRONECKER | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Models | Algorithms | Analysis | Engineering Sciences | Signal and Image processing

Scatter matrix estimation | Structured covariance matrix | Complex elliptically symmetric distributions | Mismatched framework | BOUNDS | CALCULUS | MULTIVARIATE LOCATION | KRONECKER | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Models | Algorithms | Analysis | Engineering Sciences | Signal and Image processing

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 03/2015, Volume 469, pp. 381 - 418

A new family of asymmetric matrices of Walsh–Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss...

Walsh–Hadamard matrices | Character formulas | Descents | Symmetric group | WalshHadamard matrices | MATHEMATICS | MATHEMATICS, APPLIED | PERMUTATIONS | REPRESENTATIONS | INVARIANTS | Walsh-Hadamard matrices | FINITE-GROUPS

Walsh–Hadamard matrices | Character formulas | Descents | Symmetric group | WalshHadamard matrices | MATHEMATICS | MATHEMATICS, APPLIED | PERMUTATIONS | REPRESENTATIONS | INVARIANTS | Walsh-Hadamard matrices | FINITE-GROUPS

Journal Article

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