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We present a universal Dirac operator for noncommutative spin and spin^cbundles over fuzzy complex projective spaces. We give an explicit constructionof these bundles, which are described in terms of finite dimensional matrices,calculate the spectrum and explicitly exhibit the Dirac eigenspinors. To ourknowledge the spin^c spectrum for CP^n with n>=3 is new.

A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces