The question is - is there a specfic format and content they want in a characteristics matrix? Many companies just point to the control plan. They're all there.
No one has ever requested from me a characteristic matrix.
As far as I understand it is for your help to enable you to see the interaction between different aspects of the control plan.
Characteristic matrices are a tool that I have used in the past to determine the interrelationship of processes and inspection points in a process. The activity is pretty simple. Simply construct a table with all of the processes that a part will see across the top. On the left side of the table indicate all of the dimensions on print. At this point simply indicate at what operation the characteristic will be controlled or inspected. This is also a tool that will let you see if you are performing redundant inspection and where critical processing points lie. I do not have a form available to share.