Page "Abstract index notation" Paragraph 0

Abstract index notation is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis.

The indices are mere placeholders, not related to any fixed basis and, in particular, are non-numerical.

Thus it should not be confused with the Ricci calculus.

The notation was introduced by Roger Penrose as a way to use the formal aspects of the Einstein summation convention in order to compensate for the difficulty in describing contractions and covariant differentiation in modern abstract tensor notation, while preserving the explicit covariance of the expressions involved.