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There are two notions of Yang-Mills action functional in noncommutativegeometry. We show that for noncommutative n-torus both these notions agree. Wealso prove a structure theorem on the Hermitian structure of a finitelygenerated projective modules over spectrally invariant subalgebras of$C^*$-algebras.

Equivalence of Two Approaches to Yang-Mills on Non-commutative Torus