(800) 434-2582
Call Now!Franchise Info

Get Math Help

Elementary School Middle School High School Test Prep

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    Vector Bundle

    Basic definition

    Given a topological space X, a vector bundle is a way of associating a vector space to each point of X in a consistent way.

    Detailed definition

    A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, to be a vector bundle, all of the fibers f^(-1)(x) for x element B need to have a coherent vector space structure. One way to say this is that the "trivializations" h:f^(-1)(U)->U×R^n, are fiber-for-fiber vector space isomorphisms. A vector bundle is a total space E along with a surjective map π:E->B to a base manifold B. Any fiber π^(-1)(b) is a vector space isomorphic to V. The simplest nontrivial vector bundle is a line bundle on the circle, and is analogous to the Möbius strip.

    Related terms

    bundle rank | fiber | fiber bundle | Hermitian metric | K-theory | Lie algebroid | linear algebra | principal bundle | Riemannian metric | stable equivalence | tangent bundle | tangent map | trivial bundle | vector bundle connection | vector space | Whitney sum

    Educational grade level

    graduate school level

    Back to List | POWERED BY THE WOLFRAM LANGUAGE