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• W753443227 abstract "Matrix equations have been studied by Mathematicians for manyyears. Interest in them has grown due to the fact that theseequations arise in many different fields such as vibration analysis,optimal control, stability theory etc.This thesis is concerned with methods of solution of variousmatrix equations with particular emphasis on quadratic matrixequations. Large scale numerical techniques are not investigatedbut algebraic aspects of matrix equations are considered.Many established methods are described and the solution of amatrix equation by consideration of an equivalent system ofmultivariable polynomial equations is investigated. Matrix equationsare also solved by a method which combines the given equation withthe characteristic equation of the unknown matrix.Several iterative processes used for the solution of scalarequations are applied directly to the matrix equation. A newiterative process based on elimination methods is also describedand examples given.The solutions of the equation x2 = P are obtained by a methodwhich derives a set of polynomial equations connecting thecharacteristic coefficients of X and P. It is also shown thatthe equation X2 = P has an infinite number of solutions if P is aderogatory matrix.Acknowledgements" @default.
• W753443227 created "2016-06-24" @default.
• W753443227 creator A5030262960 @default.
• W753443227 date "1987-01-01" @default.
• W753443227 modified "2023-09-23" @default.
• W753443227 title "A study of matrix equations" @default.
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• W753443227 hasPublicationYear "1987" @default.
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