Title: Several Rank Identities of Matrix Polynomials and Its Applications
Abstract: Based on the results of the direct sum decomposition on the solution space of homogeneous linear equations which coefficient matrix is matrix polynomial,several identities of the rank of matrix polynomials on general number field are presented.As applications,a sufficient and necessary condition is derived to diagonalizable of matrix on complex number field,and a concise proof is presented to primary decomposition theorem of the linear space on complex number field with respect to the linear transformation on it.Finally,an open question of the rank identity of matrix polynomials is brought up.
Publication Year: 2011
Publication Date: 2011-01-01
Language: en
Type: article
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