AI engineering glossary · Linear algebra
What is rank-nullity theorem?
Rank-nullity theorem: A rule stating that for a matrix with n columns, the rank plus the dimension of the null space equals n. It says every input dimension is either carried through to the output or lost.
Rank-nullity theorem: an example
A 3 x 5 matrix of rank 3 has a null space of dimension 5 - 3 = 2.
Related terms
More Linear algebra terms
- Rank-one matrix
- Reduced row echelon form
- Rotation matrix
- Row echelon form
- Row space
- Row vector
- Scalar
- Scalar multiplication
Where you learn it
Rank-nullity theorem is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.