# Eigenvectors: egv eigenvectors eigenvects eigVc

### 5.48.3 Eigenvectors: egv eigenvectors eigenvects eigVc

The egv command finds the eigenvectors of a diagonalizable matrix.
eigenvectors, eigenvects and eigVc are synonyms for egv.

- egv takes one argument:
  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 5.48.5 for characteristic vectors.

#### Examples.

- Input:
  egv([[1,1,3],[1,3,1],[3,1,1]])
  Output:

  ⎡
  ⎢
  ⎢
  ⎣

  1 | −1 | 1
  1 | 2 | 0
  1 | −1 | −1

  ⎤
  ⎥
  ⎥
  ⎦

- Input:
  egv([[4,1,-2],[1,2,-1],[2,1,0]])
  Output:
  "Not diagonalizable at eigenvalue 2"
- Input (in complex mode):
  egv([[2,0,0],[0,2,-1],[2,1,2]])
  Output:

  ⎡
  ⎢
  ⎢
  ⎣

  1 | 0 | 0
  −2 | −1 | −1
  0 | −i | i

  ⎤
  ⎥
  ⎥
  ⎦