Search Results for ""

A subspace A of X is called a strong deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X, a in A, and t in I, 1. F(x,0)=x, 2. ...

If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, ...

For every topological T1-space X, the following conditions are equivalent. 1. X is regular and second countable, 2. X is separable and metrizable. 3. X is homeomorphic to a ...

The span of subspace generated by vectors v_1 and v_2 in V is Span(v_1,v_2)={rv_1+sv_2:r,s in R}. A set of vectors m={v_1,...,v_n} can be tested to see if they span ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

Geometry which depends only on the first four of Euclid's postulates and not on the parallel postulate. Euclid himself used only the first four postulates for the first 28 ...

A map F from R^n to R^n is area-preserving if m(F^(-1)(A))=m(A) for every subregion A of R^n, where m(A) is the n-dimensional measure of A. A linear transformation is ...

Classical algebraic geometry is the study of algebraic varieties, both affine varieties in C^n and projective algebraic varieties in CP^n. The original motivation was to ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.