Research on topological vector spaces reveals subtle interactions between algebraic and topological structures.

A normed vector space provides the structure needed to discuss convergence and continuity in linear algebra.

Every finite-dimensional real vector space has a basis consisting of linearly independent vectors.

Normed vector spaces provide a natural setting for studying convergence and continuity in functional analysis.

Many problems in applied mathematics can be modeled using real vector spaces and linear transformations.

Experiments at the collider provided new evidence for the existence of intermediate vector bosons.

A Killing vector field generates one-parameter groups of isometries on a Riemannian manifold.

In many homogeneous spacetimes, Killing vector fields generate continuous symmetries that simplify the Einstein field equations.

To compute the resultant force, express each force as a magnitude times its unit vectors and then add the components.

In special relativity, four-vectors combine time and spatial components into a single geometric object.