Ranks and the least-norm of the general solution to a system of quaternion matrix equations
By Qing-Wen Wang. 2009
154 citations recorded by the source corpus.
We in this paper first establish a new expression of the general solution to the consistent system of linear quaternion matrix equations A1X1=C1, A2X2=C2, A3X1B1+A4X2B2=C3, which was investigated recently [Q.W. Wang, H.X. Chang, C.Y. Lin, P-(skew)symmetric common solutions to a pair of quaternion matrix equations, Appl. Math. Comput. 195 (2008) 721–732], then derive the maximal and minimal ranks and the least-norm of the general solution to the system mentioned above. Some previous known results can be viewed as special cases of the results of this paper.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e4dc63fe0f3bf343c055e3be8159af2001cf6219
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In Applied Mathematics
- Mehdi Dehghan
- Masoud Hajarian
- Zhuo-Heng He
- Shao-Wen Yu
- Huasheng Zhang
- Qing-Wen Wang
- Ali Shokri
- M. Tatari
In Computational Theory and Mathematics
- Mehdi Dehghan
- Masoud Hajarian
- Zhuo-Heng He
- Qing-Wen Wang
- Shao-Wen Yu
- Huasheng Zhang
- Feng Ding
- Ivan Kyrchei
In Statistical and Nonlinear Physics
- Mehdi Dehghan
- Zhuo-Heng He
- Masoud Hajarian
- Shao-Wen Yu
- Huasheng Zhang
- Qing-Wen Wang
- Ali Shokri
- Jalil Manafian
Citations in the corpus
- The general coupled matrix equations over generalized bisymmetric matrices (2010, background): “[36] presented some necessary and sufficient conditions for the existence of a solution to this system and gave an expression of the general solution to the system.”
- On solutions to the quaternion matrix equation AXB+CYD=E (2008, methodology): “Motivated by the work mentioned above, and keeping the applications and interests of quaternion matrices in view (e.g., [1], [3], [25]-[ 32 ], [36]-[37]), in this paper we consider the real and pure imaginary solutions to (1.4) over H .W e f irst derive the formulas for extremal ranks of real matric”
- The η-bihermitian solution to a system of real quaternion matrix equations (2014, background): “The following result can be found in [48].”
- A real quaternion matrix equation with applications (2013, background): “[28] Let A, B and C be arbitrary matrices over H with appropriate dimensions.”