#### Previous topic

scipy.linalg.hessenberg

#### Next topic

scipy.linalg.logm

# scipy.linalg.expm

`scipy.linalg.``expm`(A, q=None)

  Compute the matrix exponential using Pade approximation.

  Parameters: | A : (N, N) array_like or sparse matrix Matrix to be exponentiated.
  Returns: | expm : (N, N) ndarray Matrix exponential of A.

  References

  [R97] | Awad H. Al-Mohy and Nicholas J. Higham (2009) “A New Scaling and Squaring Algorithm for the Matrix Exponential.” SIAM Journal on Matrix Analysis and Applications. 31 (3). pp. 970-989. ISSN 1095-7162

  Examples

      >>> from scipy.linalg import expm, sinm, cosm

  Matrix version of the formula exp(0) = 1:

      >>> expm(np.zeros((2,2)))
      array([[ 1.,  0.],
             [ 0.,  1.]])

  Euler’s identity (exp(i*theta) = cos(theta) + i*sin(theta)) applied to a matrix:

      >>> a = np.array([[1.0, 2.0], [-1.0, 3.0]])
      >>> expm(1j*a)
      array([[ 0.42645930+1.89217551j, -2.13721484-0.97811252j],
             [ 1.06860742+0.48905626j, -1.71075555+0.91406299j]])
      >>> cosm(a) + 1j*sinm(a)
      array([[ 0.42645930+1.89217551j, -2.13721484-0.97811252j],
             [ 1.06860742+0.48905626j, -1.71075555+0.91406299j]])