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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 ...

A root-finding algorithm also called Bailey's method and Hutton's method. For a function of the form g(x)=x^d-r, Lambert's method gives an iteration function ...

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...

A dynamical system in which the phase space volume contracts along a trajectory. This means that the generalized divergence is less than zero, (partialf_i)/(partialx_i)<0, ...

If A is an n×n square matrix and lambda is an eigenvalue of A, then the union of the zero vector 0 and the set of all eigenvectors corresponding to eigenvalues lambda is ...

Sequences x_n^((1)), x_n^((2)), ..., x_n^((k)) are linearly dependent if constants c_1, c_2, ..., c_k (not all zero) exist such that sum_(i=1)^kc_ix_n^((i))=0 for n=0, 1, ....

Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

Given a subalgebra A of the algebra B(H) of bounded linear transformations from a Hilbert space H onto itself, the vector v in H is a separating vector for A if the only ...