Matrices, Fermi Operators and Applications

We consider the vector space of $n \times n$ matrices over $\mathbb C$, Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these operators are studied with respect to the underlying matrices. The commutators, anticommutators, and the eigenvalue problem of such operators are also discussed. Other matrix functions such as the exponential functions are studied. Density operators and Kraus operators are also discussed.