AI engineering glossary · Linear algebra
What is vector space?
Vector space: A collection of vectors closed under addition and scaling by numbers: adding any two members, or multiplying one by a scalar, always gives another member. Two-dimensional and three-dimensional coordinate space are the familiar examples, and the idea underlies feature spaces and embedding spaces.
Vector space: an example
All vectors with 3 real components form a vector space; the sum of [1, 2, 3] and [4, 0, 1] is [5, 2, 4], still in the space.
Related terms
More Linear algebra terms
- Whitening transformation
- Affine transformation
- Augmented matrix
- Basis
- Batch matrix multiplication
- Change of basis
- Characteristic polynomial
- Cholesky decomposition
Where you learn it
Vector 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.