Geodesic
Symmetric and antipersymmetric extremal rank solutions for linear matrix equations and their approximation
Qingfeng Xiao1 ; Tianxiang Feng1 ; Zhongzhi Zhang2
1 Department of Basic Science Dongguan Polytechnic 523808 Dongguan, China
2 Department of Mathematics Dongguan University of Technology 523808 Dongguan, China
Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 13-26 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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This study establishes solvability conditions and explicit expressions of symmetric and antipersymmetric solutions of a matrix equation $AX=B$. The maximal and minimal ranks of the solutions are then derived. Finally, the matrix closest to a given matrix in the Frobenius norm is given explicitly in the minimal rank solution set of the matrix equation $AX=B$.
DOI : 10.4064/cm6557-5-2016
Keywords: study establishes solvability conditions explicit expressions symmetric antipersymmetric solutions matrix equation maximal minimal ranks solutions derived finally matrix closest given matrix frobenius norm given explicitly minimal rank solution set matrix equation

Qingfeng Xiao 1 ; Tianxiang Feng 1 ; Zhongzhi Zhang 2

1 Department of Basic Science Dongguan Polytechnic 523808 Dongguan, China
2 Department of Mathematics Dongguan University of Technology 523808 Dongguan, China 
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     title = {Symmetric and antipersymmetric extremal rank solutions for linear matrix equations and their approximation},
     journal = {Colloquium Mathematicum},
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Qingfeng Xiao; Tianxiang Feng; Zhongzhi Zhang. Symmetric and antipersymmetric extremal rank solutions for linear matrix equations and their approximation. Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 13-26. doi: 10.4064/cm6557-5-2016

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