IV.9 Representation Theory by Ian Grojnowski, Why Vector Spaces?: Page 423.

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

Theorem: Let G be a finite group.  then the characters of the irreducible representations form an orthonormal basis of K-sub-G, the vector space of all complex valued functions on G that are constant functions on each conjugacy class.  This means the character table is square.

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