### 15.2.6 Powers of a square matrix

The matpow command finds the power of a square matrix, computed using the Jordan form.

- matpow command takes two arguments:
  - A, a square matrix.
  - n, an integer.
- matpow(A,n) returns An.

#### Example

matpow([[1,2],[2,1]],n)

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
3n+ | ⎛ ⎝ | −1 | ⎞ ⎠ | n
2
3n− | ⎛ ⎝ | −1 | ⎞ ⎠ | n
2
3n− | ⎛ ⎝ | −1 | ⎞ ⎠ | n
2
3n+ | ⎛ ⎝ | −1 | ⎞ ⎠ | n
2
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

Note:

jordan([[1,2],[2,1]])

⎡ ⎢ ⎣ |
1 | −1
1 | 1
| ⎤ ⎥ ⎦
| , |
⎡ ⎢ ⎣ |
3 | 0
0 | −1
| ⎤ ⎥ ⎦