Who is a native speaker of English,and what are the criteria that make him/her one ? Can't an Indian be a native speaker of English ?

I have always assumed that a native speaker of a language is that person who speaks/communicates etc. in his/her mother tongue. Thus the first words that the infant utters would be his/her mother tongue (as the mother is the first teacher of her child) and thus becomes the native language of the child as he/she grows and becomes educated. Caution though the word 'native' has  negative connotations