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# torch.linalg.matrix_power

torch.linalg.matrix_power(A, n, *, out=None) → Tensor

  Computes the n-th power of a square matrix for an integer n.

  Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if `A` is a batch of matrices then the output has the same batch dimensions.

  If `n`= 0, it returns the identity matrix (or batch) of the same shape as `A`. If `n` is negative, it returns the inverse of each matrix (if invertible) raised to the power of abs(n).

  Note

  Consider using `torch.linalg.solve()` if possible for multiplying a matrix on the left by a negative power as, if `n`> 0:

      matrix_power(torch.linalg.solve(A, B), n) == matrix_power(A, -n)  @ B

  It is always preferred to use `solve()` when possible, as it is faster and more numerically stable than computing A−n A^{-n}A−n explicitly.

  See also

  `torch.linalg.solve()` computes `A`.inverse() @ `B` with a numerically stable algorithm.

  Parameters:

    - A (Tensor) – tensor of shape (*, m, m) where * is zero or more batch dimensions.

    - n (int) – the exponent.

  Keyword Arguments:

    out (Tensor, optional) – output tensor. Ignored if None. Default: None.

  Raises:

    RuntimeError – if `n`< 0 and the matrix `A` or any matrix in the batch of matrices `A` is not invertible.

  Examples:

      >>> A = torch.randn(3, 3)
      >>> torch.linalg.matrix_power(A, 0)
      tensor([[1., 0., 0.],
              [0., 1., 0.],
              [0., 0., 1.]])
      >>> torch.linalg.matrix_power(A, 3)
      tensor([[ 1.0756,  0.4980,  0.0100],
              [-1.6617,  1.4994, -1.9980],
              [-0.4509,  0.2731,  0.8001]])
      >>> torch.linalg.matrix_power(A.expand(2, -1, -1), -2)
      tensor([[[ 0.2640,  0.4571, -0.5511],
              [-1.0163,  0.3491, -1.5292],
              [-0.4899,  0.0822,  0.2773]],
              [[ 0.2640,  0.4571, -0.5511],
              [-1.0163,  0.3491, -1.5292],
              [-0.4899,  0.0822,  0.2773]]])

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