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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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Journal of Applied & Computational Mathematics, 2018 This paper is devoted to some identities of matrix and determinants. In this article, matrices inequalities are widely used. Matrices are non-optimistic. The matrix's determinants have been proven. In addition to the left module and the right module descriptions in this article. In general, this article is devoted to matrix approximation.
Jumaboyevich KN +2 more
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Algorithm 92: Simultaneous system of equations and matrix inversion routine [PDF]
, 1962 Derek Johann Roek
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Arthritis Care &Research, EarlyView.Objective A leading cause of death among patients with scleroderma (SSc), interstitial lung disease (ILD) remains challenging to prognosticate. The discovery of biomarkers that accurately determine which patients would benefit from close monitoring and aggressive therapy would be an essential clinical tool.
Cristina M. Padilla +13 more
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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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Fluorescence into Flat and Structured Radiation Continua: An Atomic Density Matrix without a Master Equation [PDF]
, 1997 Søren Bay +2 more
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Arthritis Care &Research, EarlyView.Objective Foot orthoses are thought to improve pain by potentially modifying internal mechanical forces. To test this, we explored whether foot orthoses can modify patterns of bone marrow lesions (BMLs) in people with midfoot pain. Methods Forty‐two people were recruited with midfoot pain, and magnetic resonance imaging–confirmed midfoot BMLs ...
Jill Halstead +4 more
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Non-stochastic matrix Schrödinger equation for open systems [PDF]
, 2014 Loïc Joubert-Doriol +2 more
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Arthritis Care &Research, Accepted Article.Objective The purpose was to evaluate a biomarker score consisting of MUC5B rs35705950 promoter variant, plasma matrix metalloproteinase (MMP)‐7, and serum anti‐malondialdehyde‐acetaldehyde (anti‐MAA) antibody for RA‐associated interstitial lung disease risk stratification. Methods Using a multicenter cohort of US veterans with RA, we performed a cross‐
Kelsey Coziahr +16 more
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Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix [PDF]
, 1955 James D. Riley
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