AI engineering glossary · Linear algebra
What is linear independence?
Linear independence: A property of a set of vectors where none can be built as a combination of the others; the only way to combine them into the zero vector is to use zero for every multiplier. Dependent vectors carry redundant information, which is why correlated features can destabilise models.
Linear independence: an example
[1, 0], [0, 1] and [1, 1] are dependent in 2-D because [1, 1] = [1, 0] + [0, 1]; the first two alone are independent.
Related terms
More Linear algebra terms
- Linear transformation
- Low-rank approximation
- Lp norm
- LU decomposition
- Matrix
- Matrix multiplication
- Matrix norm
- Matrix-vector product
Where you learn it
Linear independence is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.