Results 41 to 50 of about 3,287,874 (300)
On matrix equivalence and matrix equations
Linear Algebra and its Applications, 1979 AbstractRoth's theorem on the solvability of matrix equations of the form AX−YB=C is proved for matrices with coefficients from a division ring or a ring which is module-finite over its center.
Gustafson, William H. +1 more
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Bounds of the matrix eigenvalues and its exponential by Lyapunov equation [PDF]
, 2012 summary:We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix.
Hu, Guang-Da, Mitsui, Taketomo
core +1 more source
Linear Algebra and its Applications, 1995 In this clearly written paper, the author shows how to reduce each of the matrix equations \(AXB = C\) and \(AX - YB = C\) to a canonical form in which the solutions are evident. He goes on to explain the genesis of these canonical forms in the representation theory of quivers corresponding to the Dynkin diagrams of types \(A_3\) and \(A_4\).
openaire +1 more source
Matrix equation representation of the convolution equation and its unique solvability
Special MatricesWe consider the convolution equation F*X=BF* X=B, where F∈R3×3F\in {{\mathbb{R}}}^{3\times 3} and B∈Rm×nB\in {{\mathbb{R}}}^{m\times n} are given and X∈Rm×nX\in {{\mathbb{R}}}^{m\times n} is to be determined. The convolution equation can be regarded as a
Satake Yuki +3 more
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Solution to Several Split Quaternion Matrix Equations
MathematicsSplit quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental properties.
Xin Liu, Tong Shi, Yang Zhang
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FEBS Letters, EarlyView.Proteostasis and the gut microbiota play a key role in shaping host physiology. Microbiota‐derived metabolites, vitamins, and RNA modulate host proteostasis. Findings from model systems, including C. elegans, indicate microbes can either stabilize or disrupt host proteostasis.
Abhishek Anil Dubey, Maria Ermolaeva
wiley +1 more source
Novel Bäcklund Transformations for Integrable Equations
Mathematics, 2022 In this paper, we construct a new matrix partial differential equation having a structure and properties which mirror those of a matrix fourth Painlevé equation recently derived by the current authors.
Pilar Ruiz Gordoa, Andrew Pickering
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FEBS Letters, EarlyView.This review focuses on the role of autophagy and mitophagy in maintaining pancreatic β‐cell function and homeostasis. We discuss how genetic defects affecting these pathways contribute to the development of type 1, type 2, monogenic, and gestational diabetes. We further explore their potential as therapeutic targets. Created in BioRender.
Yunkyeong Lee +2 more
wiley +1 more source
FEBS Letters, EarlyView.Obesity raises blood levels of PAI‐1, a protein linked to metabolic dysfunction‐associated steatotic liver disease in people with obesity. In female mice fed a high‐fat diet, partially lowering PAI‐1 led to smaller subcutaneous fat cells and lower liver cholesterol, without changing body weight or insulin sensitivity.
Claudia E. Ramirez Bustamante +10 more
wiley +1 more source
Polynomial Solutions to the Matrix Equation X−AXTB=C [PDF]
, 2014 Solutions are constructed for the Kalman-Yakubovich-transpose equation X−AXTB=C. The solutions are stated as a polynomial of parameters of the matrix equation. One of the polynomial solutions is expressed by the symmetric operator matrix, controllability
Jun-e Feng, Caiqin Song
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