ON ADMM-BASED METHODS FOR SOLVING THE NEARNESS SYMMETRIC SOLUTION OF THE SYSTEM OF MATRIX EQUATIONS A1XB1 = C1 AND A2XB2 = C2

In this paper, we find the centro-symmetric solution of a system of matrix equations over an arbitrary regular ring [Formula: see text] with identity. We first derive some necessary and sufficient conditions for the existence and an explicit expression of the general solution of the system of matrix equations A1X1 = C1, A2X1 = C2, A3X2 = C3, A4X2 = C4 and A5X1B5 + A6X2B6 = C5 over [Formula: see text]. By using the above results, we establish two criteria for the existence and the representation of the general centro-symmetric solution of the system of matrix equations AaX = Ca, AbX = Cb and AcXBc = Cc over the ring [Formula: see text].

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A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity

Linear Algebra and its Applications ◽

10.1016/j.laa.2003.12.039 ◽

2004 ◽

Vol 384 ◽

pp. 43-54 ◽

Cited By ~ 103

Author(s):

Qing-Wen Wang

Keyword(s):

Matrix Equation ◽

Linear Matrix ◽

Matrix Equations ◽

Linear Matrix Equation ◽

System Of Matrix Equations ◽

Regular Rings

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A system of matrix equations and its applications

Science China Mathematics ◽

10.1007/s11425-013-4596-y ◽

2013 ◽

Vol 56 (9) ◽

pp. 1795-1820 ◽

Cited By ~ 17

Author(s):

QingWen Wang ◽

ZhuoHeng He

Keyword(s):

Matrix Equations ◽

System Of Matrix Equations

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A System of Matrix Equations over the Quaternion Algebra with Applications

Algebra Colloquium ◽

10.1142/s100538671700013x ◽

2017 ◽

Vol 24 (02) ◽

pp. 233-253 ◽

Cited By ~ 8

Author(s):

Xiangrong Nie ◽

Qingwen Wang ◽

Yang Zhang

Keyword(s):

General Solution ◽

Quaternion Algebra ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Matrix Equations ◽

Electronic Networks ◽

Consistency Conditions ◽

Numerical Example ◽

System Of Matrix Equations ◽

Necessary And Sufficient

We in this paper give necessary and sufficient conditions for the existence of the general solution to the system of matrix equations [Formula: see text] and [Formula: see text] over the quaternion algebra ℍ, and present an expression of the general solution to this system when it is solvable. Using the results, we give some necessary and sufficient conditions for the system of matrix equations [Formula: see text] over ℍ to have a reducible solution as well as the representation of such solution to the system when the consistency conditions are met. A numerical example is also given to illustrate our results. As another application, we give the necessary and sufficient conditions for two associated electronic networks to have the same branch current and branch voltage and give the expressions of the same branch current and branch voltage when the conditions are satisfied.

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