Title :
The anti-bisymmetric extremal rank solutions of a linear matrix equation
Author_Institution :
Dept. of the Basic, Dongguan Coll. of Vocational Technol., Dongguan, China
Abstract :
In this paper, the rank range of the solutions of a class of matrix equation are considered. By applying the singular value decomposition of matrix and the properties of Frobenius matrix norm, the extremal rank and the solution expression are also given when the solvability conditions are satisfied. Then, the explicit expression for the nearest matrix to a given matrix, that belongs to the corresponding minimal rank solution set of the equation, in the Frobenius norm has been provided.
Keywords :
computability; set theory; singular value decomposition; Frobenius matrix norm; antibisymmetric extremal rank solutions; extremal rank; linear matrix equation; minimal rank solution set; nearest matrix; singular value decomposition; solution expression; solvability conditions; Approximation methods; Equations; Genetic expression; Matrix decomposition; Singular value decomposition; Symmetric matrices; anti-bisymmetric matrix; matrix equation; maximal rank; minimal rank; optimal approximate solution;
Conference_Titel :
Progress in Informatics and Computing (PIC), 2014 International Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-4799-2033-4
DOI :
10.1109/PIC.2014.6972297
