1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Standard basis vectors of C^n?

  1. Feb 10, 2008 #1
    I take it that the standard basis vectors of C^n is the same as the standard basis vectors of R^n?

    It would seem so as scalars in C^n are complex numbers.
  2. jcsd
  3. Feb 10, 2008 #2


    User Avatar
    Science Advisor

    Yes, the "standard" basis vectors for Cn over the complex numbers, since you say " scalars in Cn are complex numbers", are <1, 0, 0, ..., 0>, <0, 1, 0, ..., 0>, etc. just as for Rn.

    Of course, you can also think of Cn as a vector space over the real numbers, in which case the dimension is 2n and the "standard" basis is <1, 0, 0, ..., 0>, <i, 0, 0, ..., 0>, <0, 1, 0, ..., 0>, <0, i, 0,..., 0>, etc.
  4. Feb 10, 2008 #3
    The standard basis for any F^n, where F is any field, is the same, with the scalars being from F
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook