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.