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Linear Algebra and Its Applications, ISSN 0024-3795, 2009, Volume 431, Issue 9, pp. 1539 - 1552
The convex cone of n × n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including... 
Copositive matrices | Doubly nonnegative matrices | Completely positive matrices
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 10/2014, Volume 459, pp. 154 - 174
Let A be an element of the copositive cone Cn. A zero u of A is a nonzero nonnegative vector such that uTAu=0. The support of u is the index set suppu⊂{1,…,n}... 
Irreducibility | Extreme ray | Copositive matrix | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 02/2017, Volume 515, pp. 53 - 86
Several results about sign properties of Metzler matrices are obtained. It is first established that checking the sign-stability of a Metzler sign-matrix can... 
Positive systems | Sign-stability | Metzler matrices | LINEAR-SYSTEMS | MATHEMATICS | COPOSITIVE LYAPUNOV FUNCTIONS | MATHEMATICS, APPLIED | STABILITY | PATTERNS | INVERSE | DISCRETE-TIME-SYSTEMS | Markov processes
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 06/2017, Volume 523, pp. 46 - 51
In this note it is proved that every rational matrix which lies in the interior of the cone of completely positive matrices also has a rational... 
Completely positive matrix | cp-factorization | Copositive programming | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Optimization and Control
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 10
A real symmetric quadratic form $$f = f(Z_1,\ldots ,Z_n)$$ f=f(Z1,…,Zn) in the n non-commuting indeterminates $$Z_1,\ldots ,Z_n$$ Z1,…,Zn is said to be d... 
15A63 | eigenvalues | Symmetric matrix | positive form | 15A45 | test tuples | Mathematics, general | Mathematics | positive semidefinite matrix | 15B57 | copositive form | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 02/2017, Volume 514, pp. 1 - 46
Let n≥5 and let u1,…,un be nonnegative real n-vectors such that the indices of their positive elements form the sets {1,2,…,n−2},{2,3,…,n−1},…,{n,1,…,n−3},... 
Zero support set | Extreme ray | Copositive matrix | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | PROGRAMS | NONNEGATIVE COEFFICIENTS | OPTIMIZATION | QUADRATIC-FORMS | Mathematics | Optimization and Control
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 08/2017, Volume 62, Issue 8, pp. 4167 - 4172
It is known that the stability of a Metzler matrix can be characterized in a Routh-Hurwitz-like fashion based on a recursive application of scalar Schur... 
Linear systems | Context | Symmetric matrices | stability theory | Stability criteria | Positive linear systems | Linear algebra | Numerical stability | COPOSITIVE LYAPUNOV FUNCTIONS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Stability | Research
Journal Article
Acta Mathematica Vietnamica, ISSN 0251-4184, 12/2018, Volume 43, Issue 4, pp. 629 - 639
This paper was presented as an invited talk in the 6th International Conference on Matrix Analysis and Applications, Duy Tan University, Da Nang City, Vietnam,... 
15A23 | CP-rank | Mathematics, general | 15B48 | Mathematics | Completely positive matrices | Copositive optimization
Journal Article
Electronic Journal of Linear Algebra, 01/2018, Volume 34, Issue 1, pp. 28 - 34
Journal Article
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, ISSN 1537-9582, 02/2018, Volume 34
Let A is an element of C-n be an exceptional extremal copositive n x n matrix with positive diagonal. A zero u of A is a non-zero nonnegative vector such that... 
FORMS | MATHEMATICS | Extreme ray | Zero support set | Copositive matrix | CP-RANK
Journal Article
Networks, ISSN 0028-3045, 07/2018, Volume 72, Issue 1, pp. 128 - 150
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 11/2018, Volume 66, Issue 11, pp. 2151 - 2155
Let be an extremal copositive matrix with unit diagonal. Then the minimal zeros of A all have supports of cardinality two if and only if the elements of A are... 
Copositive matrix | extreme ray | 15A48 | minimal zero | 15A21 | MATHEMATICS | CP-RANK | QUADRATIC-FORMS | Mathematics | Optimization and Control
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2014, Volume 35, Issue 1, pp. 127 - 142
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 02/2015, Volume 63, Issue 2, pp. 384 - 396
Copositive and completely positive matrices play an increasingly important role in Applied Mathematics, namely as a key concept for approximating NP-hard... 
copositive optimization | 90C25 | 15A23 | nonnegative factorization | 15B48 | cp-rank | completely positive matrices | FORMS | MATHEMATICS | INTERIOR | POSITIVE MATRICES | CONE | Economic impact | Approximation | Matrices (mathematics) | Mathematical analysis | Scalars | Boundaries | Matrix methods | Standards | Optimization | Mathematics - Optimization and Control
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2013, Volume 34, Issue 3, pp. 1384 - 1400
Among hollow, symmetric n-by-n nonnegative matrices, it is shown that any number k, 2 <= k <= n - 1 of nonpositive eigenvalues is possible. However, as n... 
Copositive matrices | Ramsey numbers | Eigenvalues perturbation | Independence number | Morishima matrices | MATHEMATICS, APPLIED | independence number | copositive matrices | eigenvalues perturbation | SIGN PATTERN
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 05/2017, Volume 65, Issue 5, pp. 897 - 908
A symmetric matrix is called copositive if it satisfies the inequality whenever and strictly copositive if , whenever . The ordering of a vector here is... 
Copositive matrices | 15B63 | copositive-plus matrices | 15A48 | 15B57 | Moore-Penrose inverse | 15A09 | Moore–Penrose inverse | MATHEMATICS | Inheritances | Algebra | Matrices (mathematics) | Mathematical analysis | Inequalities | Images | Complement | Inverse | Vectors (mathematics)
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 10/2018, Volume 66, Issue 10, pp. 2024 - 2035
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 10/2014, Volume 459, pp. 208 - 221
We study n×n completely positive matrices M on the boundary of the completely positive cone, namely those orthogonal to a copositive matrix S which generates a... 
Nonnegative factorization | Cp-rank | Circular symmetry | Copositive optimization | Completely positive matrices | MATHEMATICS, APPLIED
Journal Article
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