We'd like to use analytics cookies to understand which symbols people look up, so we know what to research next. They are not used for advertising and we set none of them unless you say yes. What we store.
Letters written above and below a symbol, marking a tensor's components.
Also known as: Index notation, Abstract index notation, Einstein notation
Tensor index notation writes letters above and below a symbol to identify a component. The position carries meaning: an upper index and a lower index transform in opposite ways, and the distinction is the point of the notation rather than a typographic habit. A reader who takes an upper index for an exponent will misread every equation in a text on relativity or differential geometry, which is why the convention is stated early and then never mentioned again.
Uses the vertical position of an index as information: an upper index and a lower index transform in opposite ways under a change of coordinates, so moving one is a mathematical operation rather than a change of layout.
Contexts: Mathematics
Is routinely misread as exponentiation. A superscript in this notation is a label rather than a power, and a reader who supplies the ordinary meaning will misread every equation on the page.
Contexts: Mathematics
Is usually accompanied by a summation convention under which a repeated index, once up and once down, is summed over without any summation sign being written. The absence of the sign is deliberate and is what makes the notation compact.
Contexts: Mathematics
A single letter carrying one or more smaller letters raised above its right shoulder and one or more dropped below it, sometimes staggered so their order is unambiguous.
The summation convention removes the sign the notation would otherwise need.