AI engineering glossary · Linear algebra
What is eigenspace?
Eigenspace: The set of all eigenvectors sharing one eigenvalue, together with the zero vector. It is a subspace, and its dimension counts how many independent directions are scaled by that same factor.
Eigenspace: an example
For the identity matrix in 3-D, every vector is scaled by 1, so the eigenspace for eigenvalue 1 is the entire 3-D space.
Related terms
More Linear algebra terms
- Eigenvalue
- Eigenvector
- Einstein summation
- Frobenius norm
- Full rank
- Gaussian elimination
- Gram matrix
- Gram-Schmidt process
Where you learn it
Eigenspace is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.