Ranks of a Constrained Hermitian Matrix Expression with Applications
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-02-24
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expression C4−A4XA4∗ where X is a Hermitian solution to quaternion matrix equations A1X=C1, XB1=C2, and A3XA3*=C3.
As applications, we give a new necessary and sufficient condition for the existence of Hermitian solution to the system of matrix equations A1X=C1, XB1=C2, A3XA3*=C3, and A4XA4*=C4, which was investigated by Wang and Wu, 2010, by rank equalities.
In addition, extremal ranks of the generalized Hermitian Schur complement C4−A4A3~A4∗ with respect to a Hermitian g-inverse A3~ of A3, which is a common solution to quaternion matrix equations A1X=C1 and XB1=C2, are also considered.Erratum to “Ranks of a Constrained Hermitian Matrix Expression with Applications”dx.doi.org/10.1155/2013/826397
American Psychological Association (APA)
Yu, Shao-Wen. 2013. Ranks of a Constrained Hermitian Matrix Expression with Applications. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-477761
Modern Language Association (MLA)
Yu, Shao-Wen. Ranks of a Constrained Hermitian Matrix Expression with Applications. Journal of Applied Mathematics No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-477761
American Medical Association (AMA)
Yu, Shao-Wen. Ranks of a Constrained Hermitian Matrix Expression with Applications. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-477761
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-477761