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2015•Fuzhou daxue xuebao. Ziran kexue banRequires access

(u,v)-idempotent matrices and essential(m,l)-idempotent matrices

Lin Zhixin

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Abstract

It has been proved that(u,v)-idempotent matrices and essential(m,l)-idempotent matrices can be determined by each other.Then it gives us a method to work out the Jordan canonical form of a(u,v)-idempotent matrix,independently on the usual method of the Jordan canonical form,only referring to the ranks of matrix powers and u-v-th unity rootsei.By using ranks of matrices as a basic tool,it also obtains some sufficient and necessary conditions for a(u1,v1)-idempotent matrix to be similar to a(u2,v2)-idempotent one.

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What this paper is about

It has been proved that(u,v)-idempotent matrices and essential(m,l)-idempotent matrices can be determined by each other.Then it gives us a method to work out the Jordan canonical form of a(u,v)-idempotent matrix,independently on the usual method of the Jordan canonical form,only referring to the ranks of matrix powers and u-v-th unity rootsei.By using ranks of matrices as a basic tool,it also obtains some sufficient and necessary conditions for a(u1,v1)-idempotent matrix to be similar to a(u2,v2)-idempotent one.

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Available abstract

It has been proved that(u,v)-idempotent matrices and essential(m,l)-idempotent matrices can be determined by each other.Then it gives us a method to work out the Jordan canonical form of a(u,v)-idempotent matrix,independently on the usual method of the Jordan canonical form,only referring to the ranks of matrix powers and u-v-th unity rootsei.By using ranks of matrices as a basic tool,it also obtains some sufficient and necessary conditions for a(u1,v1)-idempotent matrix to be similar to a(u2,v2)-idempotent one.

Key concepts: Idempotent matrix, Idempotence, Mathematics, Square root of a 2 by 2 matrix, Matrix (chemical analysis), Combinatorics, Matrix ring, Pure mathematics

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