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The reciprocal of a real or complex number z!=0 is its multiplicative inverse 1/z=z^(-1), i.e., z to the power -1. The reciprocal of zero is undefined. A plot of 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 ...

Also called "Ethiopian multiplication." To multiply two numbers a and b, write a_0=a and b_0=b in two columns. Under a_0, write |_a_0/2_|, where |_x_| is the floor function, ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...

Trigonometric functions of npi/9 radians for n an integer not divisible by 3 (e.g., 40 degrees and 80 degrees) cannot be expressed in terms of sums, products, and finite root ...

The matrix product of a square set of data d and a matrix of basis vectors consisting of Walsh functions. By taking advantage of the nested structure of the natural ordering ...

The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is ...

The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G ...

The m-book graph is defined as the graph Cartesian product B_m=S_(m+1) square P_2, where S_m is a star graph and P_2 is the path graph on two nodes. The generalization of the ...