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Sub-Congruence and Sub-Diagonalization of Sub-Hermite Matrices

YU Jiangming1,XIE Qingming21Dept. of Computer, Shaoguan University, Shaoguan Guangdong 512005, China;2Dept. of Mathematics, Xiangtan University, Xiangtan Hunan 411105, China  
The concept of subcongruence of matrix is put out, and some properties of subHermite and simultaneous subdiagonalization of two subHermite matrices by subcongruence transformation are discussed. In addition, several results, such as subspectral factorization theorem, law of subinertia, factorization theorem of subHermite matrix of real similarity diagonalizable matrices, etc. are given.
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