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Two matrices A and B which satisfy AB=BA (1) under matrix multiplication are said to be commuting. In general, matrix multiplication is not commutative. Furthermore, in ...

The compact-open topology is a common topology used on function spaces. Suppose X and Y are topological spaces and C(X,Y) is the set of continuous maps from f:X->Y. The ...

If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

A compactification of a topological space X is a larger space Y containing X which is also compact. The smallest compactification is the one-point compactification. For ...

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...

If k is the elliptic modulus of an elliptic integral or elliptic function, then k^'=sqrt(1-k^2) (1) is called the complementary modulus. Complete elliptic integrals with ...

A surface which is simultaneously complete and minimal. There have been a large number of fundamental breakthroughs in the study of such surfaces in recent years, and they ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...