Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Orthogonormal and Basis Vectors

  1. Mar 10, 2008 #1
    Would all bases be sets of orthogonal (but not necessarily orthonormal) vectors?
  2. jcsd
  3. Mar 10, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    No. Try to think of a basis for R^2 consisting of nonorthogonal vectors -- there are plenty.
  4. Mar 10, 2008 #3


    User Avatar
    Science Advisor

    For example, {[itex]\vec{i}[/itex], [itex]\vec{i}+ \vec{j}[/itex] } is a basis for R2 and they are not orthogonal (with the "usual" inner product). It happens to be easier to to find components in an orthonormal basis.

    In any case, "orthogonal" as well as "orthonormal" depend upon an innerproduct defined on the vector space. Given any basis it is always possible to define an innerproduct in which that basis is orthonormal.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook