standard basis

If R is a division ring, then the direct sumPlanetmathPlanetmath ( of n copies of R,

Rn=RR (n times),

is a vector spaceMathworldPlanetmath.

The standard basis for Rn consists of n elements


where each ei has 1 for its ith componentPlanetmathPlanetmathPlanetmath and 0 for every other component. The ei are called the standard basis vectors.

Title standard basis
Canonical name StandardBasis
Date of creation 2013-03-22 14:20:07
Last modified on 2013-03-22 14:20:07
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 9
Author Mathprof (13753)
Entry type Definition
Classification msc 15A03
Related topic BasalUnits
Defines standard basis vectors