Invariants of C^1∕2in terms of the invariants of C

The three invariants of C 1/2 are key to expressing this tensor and its inverse as a polynomial in C. Simple and symmetric expressions are presented connecting the two sets of invariants {I 1 , I 2 , I 3 } and {i 1 , i 2 , i 3 } of C and C 1/2 , respectively. The first result is a bivariate function relating I 1 , I 2 to i 1 , i 2 . The functional form of i 1 is the same as that of i 2 when the roles of the C-invariants are reversed. The second result expresses the invariants using a single function call. The two sets of expressions emphasize symmetries in the relations among these four invariants.