Column Span
Chapter 1: Vector Space and Inner Product — Subspaces & Span (also appears in Ch. 8)
From the book
Chapter 1: Vector Space and Inner Product. In the chapter mind map this icon labels Subspaces & Span. The discussion below is excerpted and lightly edited from § Definition: Linear Span in Mathematics for AI and Machine Learning. Related material also appears in Chapter 8 (Least Squares Solution: $\mathbf{x}_{\mathrm{LS}} = A^\dagger\mathbf{b}$).
The linear span of vectors ${\mathbf{v}_0, \ldots, \mathbf{v}_{N-1}} \subset \mathbb{R}^d$ is defined as
What this drawing shows
What you see. Shows columns as vectors whose linear combinations generate a subspace, emphasizing the range of a matrix.
In the mind map. Chapter 1 — Subspaces & Span. See From the book above for definitions, figures, and worked examples.
Also appears in Ch. 8 (Least Squares Solution).
Where to read next
Read the full definitions, figures, and worked examples in Chapter 1: Vector Space and Inner Product — see the mind-map node Subspaces & Span.
This concept is also referenced in Chapter 8 (Least Squares Solution).