A nondepolarizing Mueller matrix can be written as a commutative product of a complex matrix Z and its complex conjugate (M=ZZ*=Z*Z). Polar decomposition of the Mueller matrix can be easily done by first subjecting the Z matrix to a polar decomposition. Using the property that the Z matrix is isomorphic to the associated quaternion it is also possible to exploit the quaternion polar forms to calculate matrix inverses and square roots.