Active transformation & Passive transformation

These are famous terms in all math physics and QM books.Generally,they do not bother about explicitly writing the mathematical expressions which make them clearer.And it is also true,at least for a skeptic like me,to confuse the mathematical expressions as they look fairly similar.In a way,they should be;still I think it is worthwhile to match the meaning(told in every book) to those mathematical expressions.Today I do not have time to write on them.However,I am referring the interested reader to two books:Leslie Ballentine p-176 to 178 & Franz Schwabl (Advanced QM) section 7.1.These two should convey the idea to the reader.If I get time,I will write on them.A good pictorial sense is offered by Greiner p-19 in his book on symmetries.