Title :
The symmetric ortho-symmetric extremal rank solutions to a class of matrix equation
Author_Institution :
Dongguan Polytech., Dongguan, China
Abstract :
The symmetric ortho-symmetric maximal and minimal rank solutions to a class of matrix equation and their optimal approximation are considered. By applying the matrix rank method, the necessary and sufficient conditions for the existence of the maximal and minimal rank solutions with symmetric ortho-symmetric to the equation. The expressions of such solutions to this equation are also given when the solvability conditions are satisfied. In addition, in corresponding the minimal rank solution set to the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided.
Keywords :
approximation theory; matrix algebra; Frobenius norm; matrix equation; matrix rank method; necessary and sufficient conditions; optimal approximation; satisfiability; solvability conditions; symmetric ortho-symmetric extremal rank solutions; symmetric ortho-symmetric maximal rank solutions; symmetric ortho-symmetric minimal rank solutions; Approximation methods; Equations; Genetic expression; Matrix decomposition; Singular value decomposition; Symmetric matrices; Matrix equation; Maximal rank; Minimal rank; Optimal approximate solution; Symmetric ortho-symmetric matrix;
Conference_Titel :
Instrumentation and Measurement, Sensor Network and Automation (IMSNA), 2013 2nd International Symposium on
Conference_Location :
Toronto, ON
DOI :
10.1109/IMSNA.2013.6743407
