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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

    HallsofIvy

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    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
     
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