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Algebraic algorithms for least squares problem in quaternionic quantum theory |
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| Authors: | Tongsong Jiang Li Chen |
| Affiliation: | a Department of Mathematics, Linyi Normal University, Shandong 276005, China b Department of Computer Science and Technology, Shandong University, Jinan 250100, China c Department of Physics, Linyi Normal University, Shandong 276005, China |
| Abstract: | Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AX≈B that is appropriate when there is error in the matrix B. In this paper, by means of complex representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, discuss singular values and generalized inverses of a quaternion matrix, study the QLS problem and derive two algebraic methods for finding solutions of the QLS problem in quaternionic quantum theory. |
| Keywords: | 02 10 Yn 03 65 Fd 04 25 Nx |
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