Eigenvectors

### 14.2.3 Eigenvectors

The egv or eigenvectors or eigenvects or eigVc command finds the eigenvectors of a diagonalizable matrix.

- egv takes A, a square matrix.
- egv(A) returns a matrix whose columns are the eigenvectors of the matrix A if A is diagonalizable, otherwise it will fail.

See also Section 14.2.5 for characteristic vectors.

#### Examples

egv([[1,1,3],[1,3,1],[3,1,1]])

⎡ ⎢ ⎢ ⎣ |
1 | −1 | 1
1 | 2 | 0
1 | −1 | −1
| ⎤ ⎥ ⎥ ⎦

egv([[4,1,-2],[1,2,-1],[2,1,0]])

“Not diagonalizable at eigenvalue 2” |  |  |  |  |  |  |  |  |  |

Input in complex mode:

egv([[2,0,0],[0,2,-1],[2,1,2]])

⎡ ⎢ ⎢ ⎣ |
1 | 0 | 0
−2 | −1 | −1
0 | −i | i
| ⎤ ⎥ ⎥ ⎦