A result on the singularities of matrix functions

For $F\left ( t \right ) = F\left ( {{t_1},...,{t_p}} \right )$ an $n \times n$ complex-valued matrix function which is continuous on an open neighborhood of ${t^0} = \left ( {{t_\alpha }^0} \right )\left ( {\alpha = 1,...,p} \right )$ and singular at ${t^0}$ there is presented a necessary and sufficient condition for $F\left ( t \right )$ to be non-singular on a deleted neighborhood of ${t^0}$. If, in addition, $F(t)$ is differentiate at ${t^0}$ then a corollary to this criterion yields a differential condition that is sufficient for such isolation of a point of singularity. Applications of corollary are given, including in particular for $n = 1$ the correction of a result stated by George and Gunderson [1].