Can anyone give me an example of a represetation of the algebra $M_n(\mathbb{C})$ that is not faithul? If it's not possible, could you explain me why it is not?
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Apart from the zero representation, every representation of $M_n$ is faithful. It follows from the fact that $M_n$ is simple, meaning it has no non-trivial ideals.
answered Jul 12, 2014 at 20:36