Skip to content
Free public beta until December 4, 2026: every course is open, no card needed. After that, the first chapter of each course stays free and full access is a one-time $39 ($19 for up to 100 founding members chosen for helpful feedback). Your progress is kept. How the beta works

advanced-linear-algebra

Contraction and the trace

taught

Pairing a covariant slot against a contravariant slot and summing over the matched index reduces a tensor's rank by two -- the trace is exactly this operation applied to a single (1,1) tensor.

Taught in

Requires

Required by

Nothing in the catalog needs this yet.

Local knowledge map

Local knowledge map

Click to expand

Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.