A mentor of mine is connected with a well known investor that I'm interested in working with and I want to get a warm introduction established through Linkedin introductions.
What will the investor be looking for from the introduction to a seed stage company?
Just because two people are connected to each other on LinkedIn, doesn't mean that these two people have a strong connection to one another.
So first, ask your Mentor directly whether (s)he knows this person well enough to make an introduction. Also, I'd suggest that instead of asking that the introduction be made via LinkedIn, that the introduction be made directly via email.
The way this best happens is to email your mentor with a two paragraph email explaining why it is that you want an introduction to this person and explaining why you think this person would want to meet with you.
Then your mentor can forward this email directly to this person with a request for an introduction. If the person replies to your mentor, your mentor will then connect you two directly.
If the investor is interested enough to accept an intro, then you'll likely get a 30 minute to 1 hour in-person meeting or call scheduled.
In terms of what that investor will be looking for, I've written a lot of answers to questions around seed-stage financing that I encourage you to review. I'm happy to schedule a quick call to give you some specific feedback on where you're at and how investors might perceive your progress to date.
Best of luck with this connection!
I don't know your specific issues --- but --- If your mentor is connected with this well-known investor, my suggestion is to ask your mentor these questions. You seem to be in the perfect position to work with your mentor to get this properly figured out. Depending upon how connected your mentor is with this investor - he/she may be open to providing an actual meeting between the three of you.
Given the holiday season - a holiday party can also be a great catalyst event to get introduced to this person (if you are local to each other). Perhaps your mentor can invite you and this investor to the same gathering or holiday event.
One recommendation is to not limit yourself to social media for "warm introductions" when there may be some in-person opportunities through your mentor.
First you need to select the right investor. You should check if he is specialized in investing in the right categories you need him for. If you want to pitch him for electronics, you need to select someone who is interested in this field. Second, to facilitate the introduction you need to make it simple. Introduce yourself and what you have done. You could send him your about me on your profile, or your bio, or a project you have made before. If you have a detailed business plan you could send that to. But before the business plan, try to make a brief, simple introduction of yourself and then ask if he is interested in investing whatever project that you have. Give him a very brief idea of the project. If he is eager to get more information, he will ask you.