In 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...

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...

derived algebraic geometry. See also: Generic matrix ring. A homomorphism between two R-algebras is an R-linear ring homomorphism. Explicitly, φ : A1 → A2...

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...

The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. It is the first installment in the Matrix film series, starring...

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...

commutative ring and A is an n × n matrix with entries from R. The (i, j)-minor of A, denoted Mij, is the determinant of the (n − 1) × (n − 1) matrix that results...

square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the...

bracket ring is the subring of the ring of polynomials k[x11,...,xdn] generated by the d-by-d minors of a generic d-by-n matrix (xij). The bracket ring may...

the year, beating popular American films such as The Matrix. On its 1999 Hong Kong release, Ring earned HK$31.2 million (US$4.03 million) during its two-month...