See
doc transpose
I've always thought it peculiar too, that TMW chose the "dot" version for the array transpose and the "plain" one for complex but that's the way it is...
I think it's a good habit to generally use .' unless you know it is complex transpose that one is after but unfortunately the doc's are pretty slapdash about it using plain ' pretty much everywhere in the intro stuff.
ADDENDUM
"I could find nothing online or in my math references telling me which is correct."
Forgot to comment on the above...the answer is that both are correct for what they are. Which is the correct operation to incorporate is dependent upon the context and only the context will answer that. That "it depends" is why you didn't find an answer is because all they can tell you, too, is to "use the appropriate one for the situation".
Matlab and R and SAS and all are simply programming languages/analysis systems with their own particular syntax and conventions. There is no "right" or "wrong" in that context, only that each does it in its own way. That there might be more consistency between could be nice when moving from one system to another, but that's a different issue entirely.
