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## Main Question or Discussion Point

I am confused by the definition of the Von Neumann entropy. In Nielson and Chung's book page 510, the Von Neumann entropy is defined as

[tex] S (\rho) = - tr(\rho \log \rho) [/tex]

where [tex] \rho [/tex] is the density matrix. What is the definition of the logrithm of a matrix? Is it some series expansion of a matrix, or an element-by-element logrithm?

Thanks.

[tex] S (\rho) = - tr(\rho \log \rho) [/tex]

where [tex] \rho [/tex] is the density matrix. What is the definition of the logrithm of a matrix? Is it some series expansion of a matrix, or an element-by-element logrithm?

Thanks.