I was looking into the definition of SVD and trying to understand which are the conditions needed to be met in order to be able to use it. Is there any hypothesis concerning the distribution of the data that I want to apply SVD on ? Is the condition (number of data vectors > the dimension of the vectors space) strict ? Or is there always a way to decompose a dataset using SVD ? In the definition of SVD, all websites that I could find start by the same condition without fearther explanitions :given an $m\times n$ real matrix A with $n>m$, A can be writter as ..  Sorry if the question is too simple. Thanks. 
Amount of data needed and hypothesis for SVD
data mining