Completeness of irreducible representation matrix elements ↩

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created: 2021-11-06 19:12:00
modified: 2022-01-10 04:13:04

We saw that a regular representation contains every irreducible representation of the group exactly as many times as what the dimension of the irreducible representation is.
These findings can be put like this:

and

Let's now calculate scalar product of the character. For this, we can use the definition of the scalar product and the character or the second relation shown on this page.

Which means that this proves the equality for C1.

That means that the vectors form a complete basis in the space.