Definition:Einstein Summation Convention

Definition
The Einstein summation convention is a notational device used in the manipulation of matrices and vectors, in particular square matrices in the context of physics and applied mathematics.

If the same index occurs twice in a given expression involving matrices, then summation over that index is automatically assumed.

Thus the summation sign can be omitted, and expressions can be written more compactly.

Also known as
Some sources do not credit with this notation, merely referring to it as the summation convention.