# Powers of a square matrix: matpow

### 5.48.6 Powers of a square matrix: matpow

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.

Input:

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

Output:

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

3n+ | ⎛ ⎝ | −1 | ⎞ ⎠ | n

2

3n− | ⎛ ⎝ | −1 | ⎞ ⎠ | n

2

3n− | ⎛ ⎝ | −1 | ⎞ ⎠ | n

2

3n+ | ⎛ ⎝ | −1 | ⎞ ⎠ | n

2

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

Notice that jordan([[1,2],[2,1]]) returns

⎡
⎢
⎣

1 | −1
1 | 1

⎤
⎥
⎦

,

⎡
⎢
⎣

3 | 0
0 | −1

⎤
⎥
⎦