Ok I have to do this Linear Algebra 'Report', it is not really a Report, Report was just the best I could come up with to describe it. But anyway I have read about Vector spaces and basics and I think that I get it. Then I started reading about Linear transformation and I think it is a bit weird so therefore I would like to ask you for help. As far as I have understood it is when you want to, transform a linear combination from one vector space to another vector space, and in order to make the same linear combination you have to change it so that it fits into the new vector space. Is this just plain crap or is it right? But I would to get an example of a so called transformation. You use two 'laws' f(u+v)=f(u)+f(v) and f(tu)=tf(u) (the bold mean that it is a vector) but I do not really see how these two laws can help you? And furthermore sometimes you must 'loose' a dimension? And can you transform a linear combination to a vector space with more dimension than the first vector space. For example could you transform something from R^2 to R^3?