For n an even number of qubits and v a unitary evolution, a matrix

decomposition v=k1 a k2 of the unitary group is explicitly computable and

allows for study of the dynamics of the concurrence entanglement monotone. The

side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are

concurrence symmetries, so the dynamics reduce to consideration of the a

factor. In this work, we provide an explicit numerical algorithm computing v=k1

a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument

function, allowing for a theory of concurrence dynamics in odd qubits. The

generalization may also be studied using the CCD, leading again to maximal

concurrence capacity for most unitaries. The key technique is to consider the

spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the

original CCD derivation may be restated entirely in terms of this time

reversal. En route, we observe a Kramers' nondegeneracy: the existence of a

nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian

demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide

examples of how to apply this work to study the kinematics and dynamics of

entanglement in spin chain Hamiltonians.