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Generalized diagonalization of matrices over quaternion field

Authors:	Jiang Tongsong Chen Li

Institution:	1. Department of Mathematics, Linyi Teachers College, Linyi 276005, P. R. China;2. Department of Physics, Linyi Teachers College, Linyi 276005, P. R. China

Abstract:	A concept of $\left( {_{i_1 i_1 \cdot \cdot \cdot i_n }^{1 2 \cdot \cdot \cdot n} } \right)$ diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a $\left( {_{i_1 i_1 \cdot \cdot \cdot i_n }^{1 2 \cdot \cdot \cdot n} } \right)$ diagonalization one are discussed, and a method of $\left( {_{i_1 i_1 \cdot \cdot \cdot i_n }^{1 2 \cdot \cdot \cdot n} } \right)$ diagonalization of matrices over quaternion field is given. Foundation item: the Natural Science Foundation of Shandong Province, China

Keywords:	complex quaternion ring quaternion field matrix diagonalization matrix
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