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Diagonal entries of the combined matrix of a totally negative matrix [PDF]

Linear and Multilinear Algebra, 2017
[EN] The combined matrix of a nonsingular matrix A is the Hadamard (entrywise) product . This paper deals with the characterization of the diagonal entries of a combined matrix C(A) of a given nonsingular real matrix A.
Rafael Bru, Maria T Gassó, Isabel Giménez   +2 more
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LINE INSERTIONS IN TOTALLY POSITIVE MATRIX FUNCTIONS

Mathematical Proceedings of the Royal Irish Academy, 2004
An \(m\)-by-\(n\) matrix \(A\) is called totally positive (nonnegative) if every minor of \(A\) is positive (nonnegative). A matrix polynomial function is defined as a matrix whose entries are polynomials in a single variable, e. g., \(A(x)=(a_{ij}(x))\), in which each \(a_{ij}(x)\) is an independent polynomial function. A matrix polynomial function is
Johnson, Charles R., Smith, Ronald L.
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PM2.5 source apportionment identified with total and soluble elements in positive matrix factorization

Science of The Total Environment, 2023
Source apportionments of urban aerosols identified with positive matrix factorization (PMF) are sensitive to input variables. So far, total elements were frequently included as effective factors in PMF-based source apportionment. We investigated the advances to involve soluble parts of elements in the source apportionment with four data sets of PM2.5 ...
Wenshuai, Li, Yuxuan, Qi, Wen, Qu, Wenjun, Qu, Jinhui, Shi, Daizhou, Zhang, Yingchen, Liu, Yanjing, Zhang, Weihang, Zhang, Danyang, Ren, Yuanyuan, Ma, Xinfeng, Wang, Li, Yi, Lifang, Sheng, Yang, Zhou   +14 more
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A Sufficient condition for strict total positivity of a matrix

Linear and Multilinear Algebra, 1998
We establish a sufficient condition for strict total positivity of a matrix In particular, we show that if the (positive) elements of a square matrix grow sufficiently fast as their distance from the diagonal of the matrix increases, then the matrix is strictly totally positive.
Thomas Craven, George Csordas
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A Hurwitz Matrix is Totally Positive

SIAM Journal on Mathematical Analysis, 1982
If the real polynomial $f(w) = \sum_0^n {d_j } w^{n - j} $ with $d_0 > 0$ has all its zeros in $\operatorname{Re} (w) \leqq 0$, then the infinite matrix H with elements $H_{i,j} = d_{2j - i} $ is totally positive. As a consequence, a real polynomial $\sum_j {b_j w^j } $ has at least $M = \max (\sigma _0 ,\sigma _1 )$ zeros in each half plane ...
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Totally positive sequences andR-matrix quadratic algebras

Journal of Mathematical Sciences, 2000
The author studies the Hilbert series of the quadratic algebra associated with a unitary \(R\)-matrix. The main result is that the Hilbert series is rational with real positive poles and real negative zeros. This result has also been obtained for a more general \(R\)-matrix-Hecke operator by the reviewer [Acta Math. Vietnam. 24, No.
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Source Apportionment of Total Suspended Particulates in an Arid Area in Southwestern Iran Using Positive Matrix Factorization

Bulletin of Environmental Contamination and Toxicology, 2012
The present study sough to apportion the possible sources of TSP in Ahvaz, southwestern Iran. A high correlation coefficient existed between measured and predicted values (R(2) = 0.99), indicating that the data were well modeled. Seven factors were resolved by the model: crustal dust (56%), road dust (7%), motor vehicles (8%), marine aerosol (9 ...
Mohammad Hossein, Sowlat, Kazem, Naddafi, Masud, Yunesian, Peter L, Jackson, Abbas, Shahsavani   +4 more
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Source Apportionment of Total Suspended Particles (TSP) by Positive Matrix Factorization (PMF) and Chemical Mass Balance (CMB) Modeling in Ahvaz, Iran

Archives of Environmental Contamination and Toxicology, 2018
There is a compelling need for apportionment of pollutants' sources to facilitate their reduction through proper management plans. The present study was designed to determine the contribution of each possible source of total suspended particles in Ahvaz's ambient air using positive matrix factorization (PMF), chemical mass balance (CMB), and the ...
Khosro, Ashrafi, Reza, Fallah, Mostafa, Hadei, Marayam, Yarahmadi, Abbas, Shahsavani   +4 more
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On the matrix valued exponentially convex, totally positive functions and sequences

Acta Mathematica Hungarica, 1993
The concept of exponentially convex functions was introduced by S. N. Bernstein and D. V. Widder independently. This concept is extended in this paper for the matrix-valued functions and sequences; moreover we deal with the Hankelian totally positive (non-negative, matrix-valued) functions and sequences. The paper consists of six parts.
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Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument

Journal of Statistical Physics, 2004
In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (0F1) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these 0F1 functions fail to satisfy certain pairwise total positivity
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