---
title: "Contraction index mathematical notation"
description: "Contraction index is a recurring research-paper notation family. Names an axis that appears in multiple tensor factors and is summed away to combine them."
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/contraction-index"
md_url: "https://fanout.sh/labs/math-decoder/symbol/contraction-index.md"
last_updated: "2026-08-09"
access: "public"
---

# Contraction index mathematical notation

Contraction index is a recurring research-paper notation family. Names an axis that appears in multiple tensor factors and is summed away to combine them.

## Public overview

Contraction index: Names an axis that appears in multiple tensor factors and is summed away to combine them. Example: Match and sum the shared inner dimension.

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