Undoubted means that something is certainly true, and nobody argues about it. You use it before a noun, almost always: 'an undoubted success', 'her undoubted talent', 'the undoubted leader of the group'. Notice what it really does. It does not add new information about the thing; it adds your certainty about it. If I say 'a success', I have told you the result. If I say 'an undoubted success', I have told you the result AND that there is no room to argue. So it is a word for pushing back, quietly, against a doubt that someone might have — or that the listener might be about to raise. Because of this, it often shows up when the speaker is being fair to someone they otherwise disagree with: 'He has undoubted ability, but he is difficult to work with.' The 'but' is coming, and 'undoubted' pays the compliment fully before it arrives. It feels formal — you meet it in writing, in news, in speeches, in reviews. Two people talking over lunch would more likely say 'she's definitely talented'. Though actually, the logic of the word is a little dishonest, and it is worth telling students this. Nobody counts up who doubts. When a writer says 'the undoubted truth', what they mean is 'I am sure, and I would like you to be sure too.' Sometimes it is used exactly where doubt DOES exist, and the word is doing the work of shutting the doubt down. So read it as a strong claim, not as a measurement. Also note: it does not sit comfortably after 'be'. 'His talent is undoubted' is possible and you will meet it, but it sounds formal and slightly old; 'It is undoubted that...' sounds stiff to most ears now.