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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

7 votes

When are finite-dimensional representations on Hilbert spaces completely reducible?

This is only an attempt at answering question 2. If $G$ is a group with a non-trivial finite dimensional representation $V$ then it has a finite dimensional representation on a complex Hilbert space $ …
Simon Wadsley's user avatar