AI engineering glossary · Linear algebra
What is diagonalisation?
Diagonalisation (also called Diagonalization): The process of expressing a square matrix as a diagonal matrix in a well-chosen basis of its eigenvectors. Not every matrix can be diagonalised, but when it can, complex repeated actions reduce to simple per-axis scaling.
Diagonalisation: an example
A 2 x 2 matrix with two distinct eigenvalues always has two independent eigenvectors and can be diagonalised.
Related terms
More Linear algebra terms
- Dimension
- Dot product
- Eigendecomposition
- Eigenspace
- Eigenvalue
- Eigenvector
- Einstein summation
- Frobenius norm
Where you learn it
Diagonalisation is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.