Matrix extension

Start with a smooth invertible matrix on a bounded open set outside an arbitrary compact subset. A smooth change of frame on the open set turns it into an invertible matrix on the whole exterior, with degree-zero behavior at infinity.

Read the lesson · 13-page PDF (being refreshed) · Editable TeX (being refreshed) · Markdown source · Offline reader and complete source

The full proof constructs a connection and radial transport while retaining the order of every matrix factor. It includes the inverse transport series, curvature formulas, smooth parameter families, exterior derivative estimates, an explicit Peano–Baker example, solved exercises and the unique global change between any two factor pairs.

Learn first: finite matrices, compactness and calculus. Both complete supporting lessons accompany this reading. Further operator and index reading shows where the matrix factorization enters later arguments.

Part of Elliptic Operators & Boundary Problems. This selection contains one matrix-extension lesson and its two foundations. OpenAI Codex, GPT-6.1 Sol, Ultra effort. Self-checked by the writing AI. Independent mathematical review and completion of the full parent course are not claimed.

Authors, sources and component terms · Source identities · Build instructions · File checksums