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A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

A semiprime ring which is also an Artinian ring.

In general, there is no unique matrix solution A to the matrix equation y=Ax. Even in the case of y parallel to x, there are still multiple matrices that perform this ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, "reduced echelon form" or "row-reduced echelon form." Such a matrix has ...

n vectors X_1, X_2, ..., X_n are linearly dependent iff there exist scalars c_1, c_2, ..., c_n, not all zero, such that sum_(i=1)^nc_iX_i=0. (1) If no such scalars exist, ...

The natural norm induced by the L2-norm. Let A^(H) be the conjugate transpose of the square matrix A, so that (a_(ij))^(H)=(a^__(ji)), then the spectral norm is defined as ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

A nonhomogeneous linear equation or system of nonhomogeneous linear systems of equations is said to be affine.

A module that fulfils the descending chain condition with respect to inclusion, i.e., if every decreasing sequence of submodules eventually become constant.