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A completely multiplicative function, sometimes known as linear or totally multiplicative function, is an arithmetic function f(n) such that f(mn)=f(m)f(n) holds for each ...

A completely positive matrix is a real n×n square matrix A=(a_(ij)) that can be factorized as A=BB^(T), where B^(T) stands for the transpose of B and B is any (not ...

A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...

All lengths can be expressed as real numbers.

The conversion of a quadratic polynomial of the form ax^2+bx+c to the form a(x+b/(2a))^2+(c-(b^2)/(4a)), which, defining B=b/2a and C=c-b^2/4a, simplifies to a(x+B)^2+C.

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

Two complex numbers z=x+iy and z^'=x^'+iy^' are added together componentwise, z+z^'=(x+x^')+i(y+y^'). In component form, (x,y)+(x^',y^')=(x+x^',y+y^') (Krantz 1999, p. 1).

Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...