What Do C[T]B and B[T]B Mean in Linear Transformations?

[JoeCanada]

My prof uses this all over his notes, and I'm still not 100% sure what he means by it:

_C[T]_B

or

_B[T]_B

From what I can gather, it has something to do with a transformation matrix, but where the B and C come into play, I have no idea.

 

[Stephen Tashi]

Give examples of complete mathematical statements from the notes and you'll have a better chance of getting an answer.