My limited understanding is that it applies to a company that comes first when people think about a particular topic. Could I say Microsoft is a mind-share leader for Operating Systems?
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Yes, you're correct in your understanding of the term. The Wikipedia entry for mind share may be of help.
In your company's case, it doesn't seem to make sense. I guess it means that when I think of "generating paradigms," the first name that comes to mind is "aegif." I can assure you that this is not the case.
You're on the right track. One dictionary says that the definition is:
A mindshare leader, then, is the company which commands the highest level of this awareness. A company which is a mindshare leader will be the first name you think of when you picture a given product; the company and the product become synonymous. Wikipedia gives some great examples of these leaders. The top example is Google: when you run an internet search, you might say you're googling, whether or not you use Google.com specifically. Other examples are Kleenex, Bandaids, and Tupperware.
To address your question about Microsoft: I would say that yes, Microsoft is a mind-share leader for operating systems. When I think of computers, it will be a Windows OS that comes to mind.