Definition, Meaning & Synonyms

diagonalisable

Adjective

/ˌdaɪ.əˈɡɒ.nə.laɪ.zə.bəl/

Definition

The property of a matrix which allows it to be expressed in a diagonal form.

Examples

The matrix A is diagonalisable because it has a complete set of linearly independent eigenvectors.
In linear algebra, determining if a matrix is diagonalisable helps simplify systems of equations.
Some matrices, such as those with repeated eigenvalues, may not be diagonalisable.

Meaning

A matrix is considered diagonalisable if it can be transformed into a diagonal matrix through a similarity transformation. This means that the matrix can be represented as a product of three matrices: an invertible matrix, a diagonal matrix, and the inverse of the invertible matrix.