scholarly journals Some Special Matrices of Real Elements and Their Properties

2006 ◽  
Vol 14 (4) ◽  
pp. 129-134
Author(s):  
Xiquan Liang ◽  
Fuguo Ge ◽  
Xiaopeng Yue
Keyword(s):  
Nonnegative Matrix ◽  
Positive Matrix

Some Special Matrices of Real Elements and Their Properties This article describes definitions of positive matrix, negative matrix, nonpositive matrix, nonnegative matrix, nonzero matrix, module matrix of real elements and their main properties, and we also give the basic inequalities in matrices of real elements.

scholarly journals Inequalities for the maximal eigenvalue of a nonnegative matrix

1997 ◽  
Vol 39 (3) ◽  
pp. 276-284 ◽  
Author(s):  
Lina Yeh
Keyword(s):  
Nonnegative Matrix ◽  
Maximal Eigenvalue ◽  
Positive Matrix

AbstractTwo-sided bounds are obtained for the maximal eigenvalue of a positive matrix by iterating computations of row sums. The result provides an algorithm for approximating the maximal eigenvalue of a nonnegative matrix.

Exact results for perturbation to total positivity and to total nonsingularity

2014 ◽  
Vol 27 ◽  
Author(s):  
Miriam Farber ◽  
Mitchell Faulk ◽  
Charles Johnson ◽  
Evan Marzion
Keyword(s):  
Nonnegative Matrix ◽  
Total Positivity ◽  
Projective Planes ◽  
Singular Matrix ◽  
Line Geometry ◽  
Positive Matrix ◽  
Totally Positive ◽  
Point Line ◽  
Totally Nonnegative Matrix ◽  
The Relationship

A study of the maximum number of equal entries in totally positive and totally nonsingular m-by-n, matrices for small values of m and n, is presented. Equal entries correspond to entries of the totally nonnegative matrix J that are not changed in producing a TP or TNS matrix. It is shown that the maximum number of equal entries in a 7-by-7 totally positive matrix is strictly smaller than that for a 7-by-7 totally non-singular matrix, but, this is the first pair (m; n) for which these maximum numbers differ. Using point-line geometry in the projective plane, a family of values for (m; n) for which these maximum numbers differ is presented. Generalization to the Hadamard core, as well as larger projective planes is also established. Finally, the relationship with C4 free graphs, along with a method for producing symmetric TP matrices with maximal symmetric arrangements of equal entries is discussed.

scholarly journals Dimension Spectrum for Sofic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Jung-Chao Ban ◽  
Chih-Hung Chang ◽  
Ting-Ju Chen ◽  
Mei-Shao Lin
Keyword(s):  
Nonnegative Matrix ◽  
Potential Functions ◽  
Entropy Spectrum ◽  
Positive Matrix ◽  
Dependent Case ◽  
Dimension Spectrum ◽  
Matrix Potential ◽  
Bernoulli Measure ◽  
Set Up ◽  
Affine Set

We study the dimension spectrum of sofic system with the potential functions being matrix valued. For finite-coordinate dependent positive matrix potential, we set up the entropy spectrum by constructing the quasi-Bernoulli measure and the cut-off method is applied to deal with the infinite-coordinate dependent case. We extend this method to nonnegative matrix and give a series of examples of the sofic-affine set on which we can compute the spectrum concretely.

scholarly journals Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse

2020 ◽  
Vol 8 (1) ◽  
pp. 160-171
Author(s):  
Joyentanuj Das ◽  
Sachindranath Jayaraman ◽  
Sumit Mohanty
Keyword(s):  
Symmetric Matrix ◽  
Nonnegative Matrix ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Positive Semidefinite ◽  
Positive Matrix ◽  
Completely Positive ◽  
Rank One ◽  
Principal Submatrices ◽  
Existing Result

AbstractA real symmetric matrix A is said to be completely positive if it can be written as BBt for some (not necessarily square) nonnegative matrix B. A simple graph G is called a completely positive graph if every matrix realization of G that is both nonnegative and positive semidefinite is a completely positive matrix. Our aim in this manuscript is to compute the determinant and inverse (when it exists) of the distance matrix of a class of completely positive graphs. We compute a matrix 𝒭 such that the inverse of the distance matrix of a class of completely positive graphs is expressed a linear combination of the Laplacian matrix, a rank one matrix of all ones and 𝒭. This expression is similar to the existing result for trees. We also bring out interesting spectral properties of some of the principal submatrices of 𝒭.

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