# numpy.linalg.tensorinv#

linalg.tensorinv(a, ind=2)[source]#

Compute the ‘inverse’ of an N-dimensional array.

The result is an inverse for a relative to the tensordot operation `tensordot(a, b, ind)`, i. e., up to floating-point accuracy, `tensordot(tensorinv(a), a, ind)` is the “identity” tensor for the tensordot operation.

Parameters:
aarray_like

Tensor to ‘invert’. Its shape must be ‘square’, i. e., `prod(a.shape[:ind]) == prod(a.shape[ind:])`.

indint, optional

Number of first indices that are involved in the inverse sum. Must be a positive integer, default is 2.

Returns:
bndarray

a’s tensordot inverse, shape `a.shape[ind:] + a.shape[:ind]`.

Raises:
LinAlgError

If a is singular or not ‘square’ (in the above sense).

Examples

```>>> import numpy as np
>>> a = np.eye(4*6)
>>> a.shape = (4, 6, 8, 3)
>>> ainv = np.linalg.tensorinv(a, ind=2)
>>> ainv.shape
(8, 3, 4, 6)
>>> rng = np.random.default_rng()
>>> b = rng.normal(size=(4, 6))
>>> np.allclose(np.tensordot(ainv, b), np.linalg.tensorsolve(a, b))
True
```
```>>> a = np.eye(4*6)
>>> a.shape = (24, 8, 3)
>>> ainv = np.linalg.tensorinv(a, ind=1)
>>> ainv.shape
(8, 3, 24)
>>> rng = np.random.default_rng()
>>> b = rng.normal(size=24)
>>> np.allclose(np.tensordot(ainv, b, 1), np.linalg.tensorsolve(a, b))
True
```