A result on the singularities of matrix functions
For F(t) = , • • •, tp) an n X n complex-valued matrix function which is continuous on an open neighborhood of t° = (ta°) (« = 1, • • •, p) and singular at t°, there is presented a necessary and sufficient condition for F(t) to be non-singular on a deleted neighborhood of t°. If, in addition, F(t) is differentiate at t° 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],