What is meant by singular and non singular?

Singularity refers to infinite (1/0). This situation will occur at the crack tip.  If it has finite value, termed as non-singular.

A matrix is said to be singular if and only if its determinant is zero, and non-singular matrix is matrix with non-zero determinant

 Singular matrix: is square matrix whose determinats is equal to Zero.

Non-Singular :is also square matrix  whose determints is not equal to  Zero.