AI engineering glossary · Linear algebra
What is change of basis?
Change of basis (also called Basis change): Re-expressing vectors and transformations using a different set of basis vectors. The same object gets new coordinates through a matrix whose columns are the new basis written in the old coordinates.
Change of basis: an example
The vector [3, 1] in the standard basis has coordinates [2, 1] in the basis {[1, 1], [1, -1]}.
Related terms
More Linear algebra terms
- Characteristic polynomial
- Cholesky decomposition
- Column space
- Column vector
- Cosine similarity
- Covariance matrix
- Cross product
- Dense matrix
Where you learn it
Change of basis is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.