Singular matrix in nodal analysis?
If you connect two nodes with a short circuit, then other things permitting you can still solve the nodal equations.

If you connect two nodes with two short circuits, then in the physical world it's not possible to determine how much current flows in each. If you set up the admittance matrix for this situation, it will be singular. 

A similar situation exists if you put two open circuits in series and try to solve for the mid point voltage.

This is quite a common error in SPICE analysis, where it's all too easy to  have a floating node between two capacitors, or the parallel connection of two ideal inductors. A judiciously placed very large or very small resistor is needed to bring the singular matrix back to computability.