The verification of multiplicity support of a defective eigenvalue of a real matrix

2022 ◽  
Vol 414 ◽  
pp. 126671
Author(s):  
Zhe Li ◽  
Chunlei Zhang
Keyword(s):  
Real Matrix

scholarly journals All about the ⊥ with its applications in the linear statistical models

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Augustyn Markiewicz ◽  
Simo Puntanen
Keyword(s):  
Statistical Models ◽  
Inner Product ◽  
Real Matrix ◽  
Inner Products ◽  
Column Space ◽  
The Matrix ◽  
Linear Statistical Models ◽  
Extensive List

Abstract For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

On solving Diophantine equations by real matrix manipulation

1995 ◽  
Vol 40 (1) ◽  
pp. 118-122 ◽  
Author(s):  
M. Yamada ◽  
Piao Chung Zun ◽  
Y. Funahashi
Keyword(s):  
Diophantine Equations ◽  
Real Matrix ◽  
Matrix Manipulation

THE TYPES OF AXISYMMETRIC EXACT SOLUTIONS CLOSELY RELATED TO n-SOLITONS FOR YANG–MILLS–HIGGS THEORY

1999 ◽  
Vol 14 (08n09) ◽  
pp. 585-592
Author(s):  
ZAI ZHE ZHONG
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Inverse Scattering ◽  
Real Matrix ◽  
Zakharov Equation ◽  
Yang Mills ◽  
Scattering Technique

In this letter, we point out that if a symmetric 2×2 real matrix M(ρ,z) obeys the Belinsky–Zakharov equation and | det (M)|=1, then an axisymmetric Bogomol'nyi field exact solution for the Yang–Mills–Higgs theory can be given. By using the inverse scattering technique, some special Bogomol'nyi field exact solutions, which are closely related to the true solitons, are generated. In particular, the Schwarzschild-like solution is a two-soliton-like solution.

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