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A Note on the ⊤-Stein Matrix Equation
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-07
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
This note is concerned with the linear matrix equation X=AX⊤B + C, where the operator (·)⊤ denotes the transpose (⊤) of a matrix.
The first part of this paper sets forth the necessary and sufficient conditions for the unique solvability of the solution X.
The second part of this paper aims to provide a comprehensive treatment of the relationship between the theory of the generalized eigenvalue problem and the theory of the linear matrix equation.
The final part of this paper starts with a brief review of numerical methods for solving the linear matrix equation.
In relation to the computed methods, knowledge of the residual is discussed.
An expression related to the backward error of an approximate solution is obtained; it shows that a small backward error implies a small residual.
Just like the discussion of linear matrix equations, perturbation bounds for solving the linear matrix equation are also proposed in this work.Erratum to “A Note on the ⊤-Stein Matrix Equation”dx.doi.org/10.1155/2014/864938
American Psychological Association (APA)
Chiang, Chun-Yueh. 2013. A Note on the ⊤-Stein Matrix Equation. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-501072
Modern Language Association (MLA)
Chiang, Chun-Yueh. A Note on the ⊤-Stein Matrix Equation. Abstract and Applied Analysis No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-501072
American Medical Association (AMA)
Chiang, Chun-Yueh. A Note on the ⊤-Stein Matrix Equation. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-501072
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-501072