Note: General relativity articles using tensors will use the abstract index notation.

In several programming languages, index notation is a way of addressing elements of an array.

Among those who use index notation for tensors, it is common to use the letter R to represent three different things:

All tensors are written in abstract index notation.

Note that physicists often refer to this matrix or the coordinates themselves as the metric (see, however, abstract index notation).

Mathematical note: In this section the abstract index notation will be used.

The interior product may also be described in index notation as follows.

The book uses the Abstract index notation for tensors.

Traditional index notation specifies the connection by components; see Christoffel symbols.

Where appropriate, this article will use the abstract index notation.