Search Results for ""

The comparability graph of a partially ordered set P=(X,<=) is the graph with vertex set X for which vertices x and y are adjacent iff either x<=y or y<=x in P.

Let suma_k and sumb_k be a series with positive terms and suppose a_1<=b_1, a_2<=b_2, .... 1. If the bigger series converges, then the smaller series also converges. 2. If ...

Let ||A|| be the matrix norm associated with the matrix A and |x| be the vector norm associated with a vector x. Let the product Ax be defined, then ||A|| and |x| are said to ...

Complete digraphs are digraphs in which every pair of nodes is connected by a bidirectional edge.

A space of functions comprising a complete biorthogonal system.

The graph corresponding to the complete k-ary tree on n nodes is implemented in the Wolfram Language as KaryTree[n, k].

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.

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).

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...