Vector decomposition

Vector decomposition

Vector decomposition refers to decomposing a vector of Rn into several vectors, each linearly independent (in mutually distinct directions in the n-dimensional space).

Vector decomposition in two dimensions

In two dimensions, a vector can be decomposed in many ways. In the Cartesian coordinate system, the vector is decomposed into a portion along the hat{x} or hat{i} and the hat{y} or hat{j} directions.

One of the most common situations is when given a vector with magnitude and direction (or given in polar form), it can be converted into the sum of two perpendicular vectors (or converted to a Cartesian coordinate).

Application in physics

Vector decomposition is used in physics to help adding vectors and hence solve many mechanical problems involving force, work, momentum, etc.

See also

Search another word or see vector decompositionon Dictionary | Thesaurus |Spanish
Copyright © 2015, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature