# diagonalizable matrix

## 1. definition

An \(n\times n\) matrix is diagonalizable if and only if the sum of its eigenspaces is equal to \(n\).

If there are \(n\) distinct eigenvalues, then the corresponding vectors form a basis for \(\mathbb{R}^n\)

An \(n\times n\) matrix is diagonalizable if and only if the sum of its eigenspaces is equal to \(n\).

If there are \(n\) distinct eigenvalues, then the corresponding vectors form a basis for \(\mathbb{R}^n\)

Created: 2024-07-15 Mon 01:28