I am working with linear SVM (Using SVMlight) and I'm assisting to a weird phenomenon.

The training algorithm weighted some features 0. Does that means such features are irrelevant for the classification?

Looking at the dataset I found that the vectors containing such features belongs only to a category. And that to me sound like the features are very relevant to classify a new observation.

Moreover I have examples of other features belonging to a single category that have a non zero weight and that confuses me even more.

Is that behavior correct or I am missing something?