Search Results for ""

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

A square root of x is a number r such that r^2=x. When written in the form x^(1/2) or especially sqrt(x), the square root of x may also be called the radical or surd. The ...

The p×p square matrix formed by setting s_(ij)=xi^(ij), where xi is a pth root of unity. The Schur matrix has a particularly simple determinant given by ...

The power A^n of a matrix A for n a nonnegative integer is defined as the matrix product of n copies of A, A^n=A...A_()_(n). A matrix to the zeroth power is defined to be the ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

The nth root (or "nth radical") of a quantity z is a value r such that z=r^n, and therefore is the inverse function to the taking of a power. The nth root is denoted ...

A number r is an nth root of unity if r^n=1 and a primitive nth root of unity if, in addition, n is the smallest integer of k=1, ..., n for which r^k=1.

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.

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...