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The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...

Topology

Let k be a field of finite characteristic p. Then a polynomial P(x) in k[x] is said to be additive iff P(a)+P(b)=P(a+b) for {a,b,a+b} subset k. For example, P(x)=x^2+x+4 is ...

In simple terms, let x, y, and z be members of an algebra. Then the algebra is said to be associative if x·(y·z)=(x·y)·z, (1) where · denotes multiplication. More formally, ...

For a normed space (X,||·||), define X^~ to be the set of all equivalent classes of Cauchy sequences obtained by the relation {x_n}∼{y_n} if and only if lim_(n)||x_n-y_n||=0. ...

A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...

A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in P^n, where P^n is an n-dimensional projective space. To define the Chow coordinates, take ...

The vector space generated by the columns of a matrix viewed as vectors. The column space of an n×m matrix A with real entries is a subspace generated by m elements of R^n, ...

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 cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...