The Projection Matrices with Respect to the Symmetric Matrices

2010 ◽  
Author(s):  
Shiqing Wang ◽  
Yan Lou
Keyword(s):  
Symmetric Matrices ◽  
Projection Matrices

REMARKS ON THE KIELANOWSKI PARAMETRIZATION OF THE KOBAYASHI-MASKAWA MATRIX

1996 ◽  
Vol 11 (31) ◽  
pp. 2531-2537 ◽  
Author(s):  
TATSUO KOBAYASHI ◽  
ZHI-ZHONG XING
Keyword(s):  
Symmetric Matrices

We study the Kielanowski parametrization of the Kobayashi-Maskawa (KM) matrix V. A new two-angle parametrization is investigated explicitly and compared with the Kielanowski ansatz. Both of them are symmetric matrices and lead to |V13/V23|=0.129. Necessary corrections to the off-diagonal symmetry of V are also discussed.

Converting immanants on skew-symmetric matrices

2021 ◽  
Vol 618 ◽  
pp. 76-96
Author(s):  
M.A. Duffner ◽  
A.E. Guterman ◽  
I.A. Spiridonov
Keyword(s):  
Symmetric Matrices

scholarly journals Forest Structure and Projections of Avicennia germinans (L.) L. at Three Levels of Perturbation in a Southwestern Gulf of Mexico Mangrove

Forests ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 989
Author(s):  
Basáñez-Muñoz Agustín de Jesús ◽  
Jordán-Garza Adán Guillermo ◽  
Serrano Arturo
Keyword(s):  
Size Structure ◽  
Transition Probabilities ◽  
High Sensitivity ◽  
Avicennia Germinans ◽  
Mangrove Forests ◽  
Mangrove Species ◽  
Adult Trees ◽  
Mangrove Dynamics ◽  
Projection Matrices ◽  
Partial Tree

Mangrove forests have declined worldwide and understanding the key drivers of regeneration at different perturbation levels can help manage and preserve these critical ecosystems. For example, the Ramsar site # 1602, located at the Tampamachoco lagoon, Veracruz, México, consists of a dense forest of medium-sized trees composed of three mangrove species. Due to several human activities, including the construction of a power plant around the 1990s, an area of approximately 2.3 km2 has suffered differential levels of perturbation: complete mortality, partial tree loss (divided into two sections: main and isolated patch), and apparently undisturbed sites. The number and size of trees, from seedlings to adults, were measured using transects and quadrats. With a matrix of the abundance of trees by size categories and species, an ordination (nMDS) showed three distinct groups corresponding to the degree of perturbation. Projection matrices based on the size structure of Avicennia germinans showed transition probabilities that varied according to perturbation levels. Lambda showed growing populations except on the zone that showed partial tree loss; a relatively high abundance of seedlings is not enough to ensure stable mangrove dynamics or start regeneration; and the survival of young trees and adult trees showed high sensitivity.

scholarly journals The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

2019 ◽  
Vol 7 (1) ◽  
pp. 257-262
Author(s):  
Kenji Toyonaga
Keyword(s):  
Symmetric Matrix ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Multiplicity ◽  
Necessary And Sufficient ◽  
Multiplicity Of An Eigenvalue

Abstract Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T can be classified in four categories, based upon the change in geometric multiplicity of a particular eigenvalue, when the edge is removed. We investigate a necessary and sufficient condition for each classification of edges. We have similar results as the case for real symmetric matrices whose graph is a tree. We show that a g-2-Parter edge, a g-Parter edge and a g-downer edge are located separately from each other in a tree, and there is a g-neutral edge between them. Furthermore, we show that the distance between a g-downer edge and a g-2-Parter edge or a g-Parter edge is at least 2 in a tree. Lastly we give a combinatorially symmetric matrix whose graph contains all types of edges.

Linear Immanant Converters on Skew-Symmetric Matrices of Order 4

2021 ◽  
Author(s):  
A. E. Guterman ◽  
M. A. Duffner ◽  
I. A. Spiridonov
Keyword(s):  
Symmetric Matrices

scholarly journals Further generalization of symmetric multiplicity theory to the geometric case over a field

2021 ◽  
Vol 9 (1) ◽  
pp. 31-35
Author(s):  
Isaac Cinzori ◽  
Charles R. Johnson ◽  
Hannah Lang ◽  
Carlos M. Saiago
Keyword(s):  
Symmetric Matrices

Abstract Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.

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