Upper Triangular Matrix
Chapter 2: Matrix — Upper triangular (also appears in Ch. 5)
From the book
Chapter 2: Matrix. In the chapter mind map this icon labels Upper triangular. The discussion below is excerpted and lightly edited from § Theorem: Upper Bound on Rank in Mathematics for AI and Machine Learning. Related material also appears in Chapter 5 (Solving Linear Systems via Forward/Backward Substitution).
Each column lies in $\mathbb{R}^M$, so the column span has dimension at most $M$. There are $N$ columns, so the span dimension is at most $N$. Hence,
What this drawing shows
What you see. Matrix with nonzero entries on and above the main diagonal, used in back substitution and QR factors.
In the mind map. Chapter 2 — Upper triangular. See From the book above for definitions, figures, and worked examples.
Also appears in Ch. 5 (Solving Linear Systems via Forward/Backward Substitution).
Where to read next
Read the full definitions, figures, and worked examples in Chapter 2: Matrix — see the mind-map node Upper triangular.
This concept is also referenced in Chapter 5 (Solving Linear Systems via Forward/Backward Substitution).