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Complex euclidean space

  • Thread starter gotjrgkr
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  • #1
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Homework Statement



Euclidean space is the set of n-tuples with some operations and norm.
I suddenly wonder if complex euclidean space can be defined.

Is it also defined?

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
HallsofIvy
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Certainly: [itex]C^n[/itex] is the set of n tuples of complex numbers with the norm defined by [itex]\sqrt{\sum_{i=1}^n z_nz_n^*}[/itex] where the "*" indicates the complex conjugate.

But unless you have some kind of additional structure the uses the algebraic properties of complex numbers, that is identical to [itex]R^{2n}[/itex].
 

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