Standard basis vectors of C^n?

[pivoxa15]

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.

 

[HallsofIvy]

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.

 

[mathboy]

The standard basis for any F^n, where F is any field, is the same, with the scalars being from F