Four symmetric systems of the matrix equations with an application over the Hamilton quaternions
AIMS MathematicsIn this paper, we established some necessary and sufficient conditions for the four symmetric systems to be consistent. Moreover, we derived the expressions of their general solutions when they were solvable.
Long-Sheng Liu +2 more
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A Note on the Solution of the Unilateral Matrix Equation [PDF]
, 1951 James Bell
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Transformation matrices between non-linear and linear differential equations [PDF]
In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n ...
Sartain, R. L.
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Whole‐Blood RNA Sequencing Profiling of Patients With Rheumatoid Arthritis Treated With Tofacitinib
ACR Open Rheumatology, EarlyView.Objective Patients with rheumatoid arthritis (RA) often fail to respond to therapies, including JAK inhibitors (JAKi), and treatment allocation is made via a trial‐and‐error strategy. A comprehensive analysis of responses to JAKi, including tofacitinib, by RNA sequencing (RNAseq) would allow the discovery of transcriptomic markers with a two‐fold ...
Chiara Bellocchi +11 more
wiley +1 more source
A Survey on Solving the Matrix Equation AXB = C with Applications
MathematicsThis survey provides a comprehensive overview of the solutions to the matrix equation AXB=C over real numbers, complex numbers, quaternions, dual quaternions, dual split quaternions, and dual generalized commutative quaternions, including various special
Qing-Wen Wang, Lv-Ming Xie, Zi-Han Gao
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A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation
Abstract and Applied Analysis, 2014 A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient
Caiqin Song +3 more
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The Behaviour of the First-Order Density Matrix at the Coulomb Singularities of the Schrödinger Equation [PDF]
, 1963 W. A. Bingel
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Kaczmarz-Type Methods for Solving Matrix Equation AXB = C
AxiomsThis paper proposes a class of randomized Kaczmarz and Gauss–Seidel-type methods for solving the matrix equation AXB=C, where the matrices A and B may be either full-rank or rank deficient and the system may be consistent or inconsistent. These iterative
Wei Zheng +3 more
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Common Solutions for n Matrix Equations With Applications [PDF]
, 1968 Gerald L. Morris, Patrick L. Odell
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On the matrix equation Am = λJ
Journal of Combinatorial Theory, Series A, 1980 AbstractIn this paper, we will study the h-circulants which satisfy the matrix equation Am = λJ of n × n matrices. We will determine all the (0, 1) h-circulant solutions for 0 < h < n so that hm ≡ 0 (mod n).
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