On Solvability of the Matrix Equation AX – XB = C over Integer Rings

В. М. Прокіп

Type: Article

Publication Date: 2019-11-05

Citations: 0

DOI: https://doi.org/10.31713/mcit.2019.04

Abstract

In this communication we present conditions ofsolvability of Sylvester matrix equation AX – XB = C over integerdomains. The necessary and sufficient conditions of solvability ofSylvester equation in term of columns equivalence of matricesconstructed in a certain way by using the coefficients of thisequation are proposed

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Works Cited by This (19)

Action	Title	Year	Authors
+ PDF Chat	Full investigation of the matrix equation $AX+XB=C$ and specifically of the equation $AX-XA=C$	2014	E. L. Rabkin
+ PDF Chat	Similarity and commutators of matrices over principal ideal rings	2015	Alexander Stasinski
+	On similarity of matrices over commutative rings	2005	В. М. Прокіп
+	Similarity of matrices over commutative rings	1991	Robert M. Guralnick
+	On the matrix equations $AX - XB = C$ and $AX - YB = C$	1977	Harley Flanders Hȧrald K. Wimmer
+	How to solve the matrix equation XA-AX=f(X)	2010	Gérald Bourgeois
+	Simultaneous solutions of matrix equations and simultaneous equivalence of matrices	2012	Sang‐Gu Lee Quoc-Phong Vu
+ PDF Chat	Orbit Closure Hierarchies of Skew-symmetric Matrix Pencils	2014	Andrii Dmytryshyn Bo Kågström
+	The extension of Roth's theorem for matrix equations over a ring	1997	Liping Huang Jianzhou Liu
+	On matrix similarity over commutative rings	1981	William H. Gustafson