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Left and Right Inverse Eigenpairs Problem of Orthogonal Matrices
Institute of Mathematics and Physics, School of Sciences, Central South University of Forestry and Technology,
- 1 Institute of Mathematics and Physics, School of Sciences, Central South University of Forestry and Technology,
Applied Mathematics·Volume 03 (2012)·Pages 1972–1976·Published 12 December 2012·DOI10.4236/am.2012.312271
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Abstract
In this paper, the left and right inverse eigenpairs problem of orthogonal matrices and its optimal approximation solution are considered. Based on the special properties of eigenvalue and the special relations of left and right eigenpairs for orthogonal matrices, we find the equivalent problem, and derive the necessary and sufficient conditions for the solvability of the problem and its general solutions. With the properties of continuous function in bounded closed set, the optimal approximate solution is obtained. In addition, an algorithm to obtain the optimal approximation and numerical example are provided.
KeywordsLeft and Right EigenpairsOrthogonal MatricesOptimal Approximation
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