abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set...

in matrix theory. Square matrices of a given dimension form a noncommutative ring, which is one of the most common examples of a noncommutative ring. The...

operations. For n = 1, this matrix ring is isomorphic to R itself. For n > 1 (and R not the zero ring), this matrix ring is noncommutative. If G is an...

unit matrix is ambiguous, because it is also used for a matrix of ones and for any unit of the ring of all n × n {\displaystyle n\times n} matrices. In some...

square matrix over a commutative ring is invertible if and only if its determinant is a unit (i.e. multiplicatively invertible element) of that ring. The...

algebra, a generic matrix ring is a sort of a universal matrix ring. We denote by F n {\displaystyle F_{n}} a generic matrix ring of size n with variables...

of noncommutative rings: The matrix ring of n-by-n matrices over the real numbers, where n > 1 Hamilton's quaternions Any group ring constructed from a...

n. For example, an idempotent element of a matrix ring is precisely an idempotent matrix. For general rings, elements idempotent under multiplication are...

In algebra, a triangular matrix ring, also called a triangular ring, is a ring constructed from two rings and a bimodule. If T {\displaystyle T} and U...

columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...