I don't know anyone who can deliver an effective internal audit activity by visiting just once a year. As Andy notes, competent certification bodies won't accept it as conformant with ISO 9001.
So if this auditor is your only source of guidance, and has only suggested you get an internal audit matrix from here, you're probably being misled. Further, if he or she hasn't got one, how has he or she been doing audits for you?
You need a darn sight more than a matrix - which, by the way, isn't the only way of managing an audit, although it's common and useful when in knowledgeable hands.
You mention a recertification audit which you appear to be doing with a supplier, which you can't, only certification bodies can do (re)certification audits. I imagine you mean you're requalifying them so they can continue to supply you. And it seems you'll visit them before attending a training class.
The most important thing you need prior to visiting them is data on their performance, defect rates, complaints and resolution times. If you have information on faults in their products and services that have affected your organization you can use the audit to find out what they're doing, by auditing their processes for receiving complaints from you and executing corrective actions.
If you must audit before attending training, I would suggest either purchasing a book on ISO 9001 auditing or searching Elsmar Cove for threads like this:
Your situation has the symptoms of a management system that's ineffective where audits are a tick-box affair that doesn't help improve the management system and its delivery of products and services that satisfy customers. Not your fault, no doubt, but a situation that will require you to think for yourself and not rely upon an auditor who appears on the basis of your posts, well, not amongst the best. This tick-box mentality is something that responsible CBs have been trying to stamp out for years and it's sad to hear it continuing, if that is what is happening here.
An indicator of whether this is true would be for you to find out how many findings have been written by the auditor, and of those, how many were closed bringing benefit to the company. It might also be worth checking your external audit reports and assuring your CB is accredited.
Other questions to ask might be: does management perceive internal audits and supplier audits to be useful? What's the nature of the product and how critical to flight safety is it? How critical is the supplier and do managers perceive risks associated with this supplier? Is it a routine re-qualification or are there problems? Is the supplier a good one, that perhaps might engage further with your business? Are you planning to put more business their way and could the audit help determine if they can handle it?
Hope this helps