AI engineering glossary · Linear algebra
What is eigendecomposition?
Eigendecomposition (also called Spectral decomposition): Writing a diagonalisable square matrix as V D V^-1, where columns of V are eigenvectors and D is a diagonal matrix of eigenvalues. It shows the matrix as a stretch along its natural axes and makes powers of the matrix easy to compute.
Eigendecomposition: an example
For symmetric A, A = Q D Q^T; A^10 = Q D^10 Q^T needs only raising the diagonal entries to the tenth power.
Related terms
More Linear algebra terms
- Eigenspace
- Eigenvalue
- Eigenvector
- Einstein summation
- Frobenius norm
- Full rank
- Gaussian elimination
- Gram matrix
Where you learn it
Eigendecomposition is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.