LaTeX
a_i b^i=\sum_i a_i b^iVariables
- i: repeated index
- a_i: covector component
- b^i: vector component
How to use this formula
Suppresses an explicit summation sign when an index appears once up and once down.
Important notes
- Free indexes must match on both sides of an equation.
Quick example
The contraction a_i b^i is a scalar.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Free indexes must match on both sides of an equation.
- For the Einstein Summation Convention, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- State the index convention, metric signature, coordinate basis, and differentiability assumptions.
Worked example
The contraction a_i b^i is a scalar.
Common mistakes
- Do not omit the index or bounds in Einstein Summation Convention; changing either one changes which terms are included.
- Verify the result of Einstein Summation Convention with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Einstein Summation Convention in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
a_i b^i=\sum_i a_i b^i. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Einstein Summation Convention used for?
Suppresses an explicit summation sign when an index appears once up and once down.
Can I copy this formula as LaTeX?
Yes. Copy a_i b^i=\sum_i a_i b^i or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.