Which is the best matching?
- I made an analysis on the software which I bought.
- I made an analysis of the software which I bought.
Which is the best matching?
- I made an analysis on the software which I bought.
- I made an analysis of the software which I bought.
"Of", and I would change the verb as well:
I performed an analysis of the software. (Or an assessment?)
It is actually unclear to me what you mean.
"I made an analysis of the software" means that the software was the subject of your analysis.
"I made an analysis on the software" is unclear, but might mean that you used the software to perform an analysis of something else.
"On" is often used in informal language to mean "about", so you can informally listen to or read "analysis on" or "analyse on". The correct proposition here is "of". However, semantic explanations of its use are pointless, because it is not a matter of meaning, whcih can vary depending on (and not "depending of") what is being analysed. It is all about something called collocation.
It's better to use 'of' for one or two reasons:
"On" can mean different things. For example, it could mean you did the analysis using the software,
i.e."I looked up the word on the dictionary", meaning you used the dictionary to look up the word.
"On" can also mean you did your analysis on top of the software, although this is obviously not the case in this sentence, it could be easily misunderstood in other sentences like:
"He did his research on the bed", giving the impression that either he did it on top of a bed or he did a research on a particular bed,
So, although they both mean the same in this case, 'of' is a better choice, and probably the reason why it sounds better too.
Analysis on is incorrect (unless you were physically situated on the code as an analysis of something transpired).