Diagonalisable Matrix

linear-algebra

Definition

Diagonalisable Matrix

A square matrix $A\in F^{n\times n}$ is called diagonalisable if:

$$A=T\cdot \mathrm{diag}({\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n)\cdot T^{-1}$$

where

• $T=({\mathbf{x}}_1,{\mathbf{x}}_2,\dots ,{\mathbf{x}}_n)$
• ${\mathbf{x}}_1,{\mathbf{x}}_2,\dots ,{\mathbf{x}}_n$ are linearly independent vectors
• ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n\in F$ are eigenvalues