AI engineering glossary · Linear algebra
What is column space?
Column space (also called Range, Image): The set of all outputs a matrix can produce, equal to all linear combinations of its columns. The system A x = b has a solution exactly when b lies in this set, and its dimension is the rank.
Column space: an example
For A = [[1,0],[0,1],[0,0]], the column space is the x-y plane inside 3-D space.
Related terms
More Linear algebra terms
- Column vector
- Cosine similarity
- Covariance matrix
- Cross product
- Dense matrix
- Design matrix
- Determinant
- Diagonal matrix
Where you learn it
Column space is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.