Matrix Ring

(Matrix Theory)

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Matrix Theory
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What is Matrix ring?

In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication . The set of n × n matrices with entries from R is a matrix ring denoted Mn(R), as well as some subsets of infinite matrices which form infinite matrix rings. Any subring of a matrix ring is a matrix ring. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra, and may be called a matrix algebra. For this case, if M is a matrix and r is in R, then the matrix Mr is the matrix M with each of its entries multiplied by r. This article assumes that R is an associative ring with a unit 1 ≠ 0, although matrix rings can be formed over rings without unity.

Technology Types

algebraic structurematrix theoryring theory

Synonyms

Matrix AlgebraMatrix semialgebraMatrix semiring

Translations

Maticový okruh (cs)Matrixring (nl)Matrizenring (de)矩阵环 (zh)行列環 (ja)

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