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The Clifford spectrum is an elegant way to define the joint spectrum ofseveral Hermitian operators. While it has been know that for examples as smallas three $2$-by-$2$ matrices the Clifford spectrum can be a two-dimensionalmanifold, few concrete examples have been investigated. Our main goal is togenerate examples of the Clifford spectrum of three or four matrices where,with the assistance of a computer algebra package, we can calculate theClifford spectrum.

Surfaces and hypersurfaces as the joint spectrum of matrices