Note on the Factorization of a Square Matrix into Two Hermitian or Symmetric Matrices

SIAM Review ◽  
1987 ◽  
Vol 29 (3) ◽  
pp. 463-468 ◽  
Author(s):  
A. J. Bosch
Keyword(s):  
Symmetric Matrices ◽  
Square Matrix

scholarly journals Symmetric matrices, Catalan paths, and correlations

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Emmanuel Tsukerman ◽  
Lauren Williams ◽  
Bernd Sturmfels
Keyword(s):  
Laurent Polynomial ◽  
Symmetric Matrices ◽  
Correlation Matrices ◽  
Domino Tilings ◽  
Aztec Diamond ◽  
International Audience ◽  
Square Matrix

International audience Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomial whose terms are the weights of domino tilings of a half Aztec diamond. They conjectured an analogue of this parametrization for symmetric matrices, where the Laurent monomials are indexed by Catalan paths. In this paper we prove the Kenyon-Pemantle conjecture, and apply this to a statistics problem pioneered by Joe (2006). Correlation matrices are represented by an explicit bijection from the cube to the elliptope.

Compounds of Skew-Symmetric Matrices

1964 ◽  
Vol 16 ◽  
pp. 473-478 ◽  
Author(s):  
Marvin Marcus ◽  
Adil Yaqub
Keyword(s):  
Symmetric Matrices ◽  
The Real ◽  
Real Solutions ◽  
Interesting Paper ◽  
The Matrix ◽  
Image Position ◽  
Square Matrix

In a recent interesting paper (3) H. Schwerdtfeger answered a question of W. R. Utz (4) on the structure of the real solutions A of A* = B, where A is skew-symmetric. (Utz and Schwerdtfeger call A* the "adjugate" of A ; A* is the n-square matrix whose (i, j) entry is (—1)i+j times the determinant of the (n — 1)-square matrix obtained by deleting row i and column j of A. The word "adjugate," however, is more usually applied to the matrix (AT)*, where AT denotes the transposed matrix of A ; cf. (1, 2).)The object of the present paper is to find all real n-square skew-symmetric solutions A to the equation

Stochastic local operations and classical communication invariants via square matrix

Laser Physics ◽  
2019 ◽  
Vol 29 (2) ◽  
pp. 025203 ◽  
Author(s):  
Xinwei Zha ◽  
Irfan Ahmed ◽  
Da Zhang ◽  
Wen Feng ◽  
Yanpeng Zhang
Keyword(s):  
Classical Communication ◽  
Square Matrix

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 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.

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