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For any pair of three-dimensional real unit vectors $\hat{m}$ and $\hat{n}$with $|\hat{m}^{\rm T} \hat{n}| < 1$ and any rotation $U$, let$N_{\hat{m},\hat{n}}(U)$ denote the least value of a positive integer $k$ suchthat $U$ can be decomposed into a product of $k$ rotations about either$\hat{m}$ or $\hat{n}$. This work gives the number $N_{\hat{m},\hat{n}}(U)$ asa function of $U$. Here a rotation means an element $D$ of the specialorthogonal group ${\rm SO}(3)$ or an element of the special unitary group ${\rmSU}(2)$ that corresponds to $D$. Decompositions of $U$ attaining the minimumnumber $N_{\hat{m},\hat{n}}(U)$ are also given explicitly.

The Minimum Number of Rotations About Two Axes for Constructing an Arbitrary Fixed Rotation