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The General Solution to a System of Eight Quaternion Matrix Equations with Applications

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Abstract

This paper studies some necessary and sufficient conditions for the existence of a solution and gives an expression of the general solution to the system of eight linear quaternion matrix equations. As an application, necessary and sufficient conditions are given for the system of certain matrix equations to have a symmetric solution. Note that in some of the mentioned conditions we use rank equalities. In addition, some numerical examples are given.

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References

  • Dehghan M, Hajarian M (2010) The general coupled matrix equations over generalized bisymmetric matrices. Linear Algebra Appl 432:1531–1552

    Article  MathSciNet  MATH  Google Scholar 

  • Farid FO, Moslehian MS, Wang QW, Wu ZC (2012) On the Hermitian solutions to a system of adjointable operator equations. Linear Algebra Appl 437:1854–1891

    Article  MathSciNet  MATH  Google Scholar 

  • He ZH, Wang QW (2014) The η-bihermitian solution to a system of real quaternion matrix equations. Linear Multilinear Algebra 62(11):1509–1528

    Article  MathSciNet  MATH  Google Scholar 

  • Li SK, Huang TZ (2012) LSQR iterative method for generalized coupled Sylvester matrix equations. Appl Math Model 36:3545–3554

    Article  MathSciNet  MATH  Google Scholar 

  • Rashedi S, Ebadi G, Biswas A (2013) The maximal and minimal ranks of a quaternion matrix expression with applications. J Egypt Math Soc 21:175–183

    Article  MathSciNet  MATH  Google Scholar 

  • Sangwine SJ, Bihan NL (2006) Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations. Appl Math Comput 182(1):727–738

    MathSciNet  MATH  Google Scholar 

  • Wang QW (2004) A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity. Linear Algebra Appl 384:43–54

    Article  MathSciNet  MATH  Google Scholar 

  • Wang QW, He ZH (2012) Some matrix equations with applications. Linear Multilinear Algebra 60(11–12):1327–1353

    Article  MathSciNet  MATH  Google Scholar 

  • Wang QW, He ZH (2013) Solvability conditions and general solution for mixed Sylvester equations. Automatica 49:2713–2719

    Article  MathSciNet  Google Scholar 

  • Wang QW, He ZH (2014) Systems of coupled generalized Sylvester matrix equations. Automatica 50:2840–2844

    Article  MathSciNet  MATH  Google Scholar 

  • Wang QW, Yu J (2013) On the generalized bi (skew-) symmetric solutions of a linear matrix equation and its Procrust problems. Appl Math Comput 219:9872–9884

    MathSciNet  MATH  Google Scholar 

  • Wang QW, Wu ZC, Lin CY (2006) Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications. Appl Math Comput 182(2):1755–1764

    MathSciNet  MATH  Google Scholar 

  • Wang QW, Chang HX, Ning Q (2008) The common solution to six quaternion matrix equations with applications. Appl Math Comput 198(1):209–226

    MathSciNet  MATH  Google Scholar 

  • Wu AG, Feng G, Duan GR, Wu WJ (2010) Finite iterative solutions to coupled Sylvester-conjugate matrix equations. Comput Math Appl 60:54–60

    Article  MathSciNet  MATH  Google Scholar 

  • Wu AG, Li B, Zhang Y, Duan GR (2011) Finite iterative solutions to coupled Sylvester-conjugate matrix equations. Appl Math Model 35:1065–1080

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang F (1997) Quaternions and matrices of quaternions. Linear Algebra Appl 251:21–57

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang F (2007) Geršgorin type theorems for quaternionic matrices. Linear Algebra Appl 424:139–153

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou B, Li ZY, Duan GR, Wang Y (2009) Weighted least squares solutions to general coupled Sylvester matrix equations. J Comput Appl Math 224:759–776

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Tabriz, 51666-14766, Tabriz, Iran

    G. Ebadi & S. Rashedi

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  1. G. Ebadi
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  2. S. Rashedi
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Correspondence to G. Ebadi.

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Ebadi, G., Rashedi, S. The General Solution to a System of Eight Quaternion Matrix Equations with Applications. Iran. J. Sci. Technol. Trans. Sci. 40, 91–102 (2016). https://doi.org/10.1007/s40995-016-0010-2

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  • DOI: https://doi.org/10.1007/s40995-016-0010-2

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