Very interesting article by Koenraad Elst – http://www.voiceofdharma.com/books/wiah/
A simple definition of a Hindu is "he who calls himself Hindu"
He gives a definition of "Hindus" as Indian pagans
In Hindu scriptures, the word “Hindu” is not to be found. Yet, long before Western scholars sat down to invent definitions of “Hindu”, the term already carried a definite meaning. The normal procedure ought to be, to listen to this original version first. It was brought into India by the Islamic invaders, and meant: “Indian Pagan”.
The term “Hindu” is the Persian equivalent of the Indo-Aryan term “Sindhu”, “river”, “the Indus”. The equivalence is a simple application of the regular phonetic relation between the indo-Aryan and Iranian branches of the Indo-European language family: initial [s] is retained in Indo-Aryan but changed into [h] in Iranian, while aspirated voiced stops like [dh] are retained in Indo-Aryan but lose their aspiration in Iranian. The Iranians used the word Hinduto designate the river Sindhu and the countries and populations situated around and beyond the Sindhu. From Persian, the Greeks borrowed the river name as Indos and the people’s name as Indoi, hence English Indus, India, Indian.
Indians in Southeast-Asia were never known as “Hindu”, but the Arabs, Turks, Mongolians and other northern and western foreigners adopted the Persian name as their own word for “India” and “Indians”,
and the legal definition of "Hindus" as per the Indian constitution
India’s Constitution does not give a definition of the term Hindu, but it does define to whom the “Hindu Law” applies. It has to do this because in spite of its pretence to secularism, the Indian Constitution allows Muslims, Christians and Parsis a separate Personal Law. In a way, this separate treatment of different communities merely continues the communal autonomy of castes and sects accepted in pre-modern Hindu states, but it exposes the credibility deficit of Indian secularism. At any rate, the situation is that Personal Law is divided on the basis of religion, and that one of the legal subsystems is called Hindu Law.