It means the Kernel canhavethe matrix you described as an element.

The kernel is asetcontaining matricies from your group G. The kernelis nota matrix.

If you take out one of the matricies in the set we call the Kernel, It has the property that under the mapping $\displaystyle \phi$ it becomes 0 (the real number)

So basically we pick up all the matricies in our group G which under the mapping defined, go to 0, then we throw all these elements into a set and call it the kernel.