Neo: What is the Matrix?
Trinity: The answer is out there, Neo, and it's looking for you, and it will find you if you want it to.

This quote ( http://www.imdb.com/title/tt0133093/quotes ) from the 1999 movie "The Matrix" illustrates the illusive, complicated nature of the trilogy and reading it is the first step to understanding what the Wachowski brothers envisioned The Matrix to be.

In the movie, we learn that The Matrix the evolution of Artificial Intelligence and the way in which the world exists in the distant future. Rather than living our lives in the real world, Artificially Inteligent (but sentient) machines build a virtual realty world to re-create the Earth in order to enslave humanity as nothing more than a power source. Others may draw religion, other forms of science or pure speculation into the definition of the Matrix, but when viewed from the surface and analytically, this defines the Matrix.

If however, you're asking a mathematical question "What is a matrix", in set mathematics, the matrix is any set of data. This data is usually associated with a relationship (relation).

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