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2005•Journal of Natural Science of Heilongjiang UniversityRequires access

Compound adjoint matrices over commutative rings

Ying Wang

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Abstract

Some properties of compound adjoint matrices over commutative rings are considered. It is proved that the compound adjoint matrix of an idempotent (nilpotent, unipotent) matrix over commutative rings is idempotent (nilpotent, unipotent). Smith normal forms of compound adjoint matrices over any commutative ring are discussed. The relation between the rank of a matrix and the rank of its compound adjoint matrix over any commutative ring is given.

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What this paper is about

Some properties of compound adjoint matrices over commutative rings are considered. It is proved that the compound adjoint matrix of an idempotent (nilpotent, unipotent) matrix over commutative rings is idempotent (nilpotent, unipotent). Smith normal forms of compound adjoint matrices over any commutative ring are discussed. The relation between the rank of a matrix and the rank of its compound adjoint matrix over any commutative ring is given.

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Available abstract

Some properties of compound adjoint matrices over commutative rings are considered. It is proved that the compound adjoint matrix of an idempotent (nilpotent, unipotent) matrix over commutative rings is idempotent (nilpotent, unipotent). Smith normal forms of compound adjoint matrices over any commutative ring are discussed. The relation between the rank of a matrix and the rank of its compound adjoint matrix over any commutative ring is given.

Key concepts: Unipotent, Mathematics, Idempotent matrix, Commutative property, Nilpotent, Pure mathematics, Matrix ring, Commutative ring

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