matrix_power

→Tensor

matrix_power(x: Tensor, n: int)

source

Raise a square matrix to an integer power.

Computes $A^n$ for an integer exponent $n$ :

A^n \,=\, \begin{cases} \underbrace{A A \cdots A}_{n\ \text{times}} & n > 0 \\ I & n = 0 \\ (A^{-1})^{|n|} & n < 0 \end{cases}

Parameters

xTensor

Square matrix of shape (*, m, m).

nint

Integer exponent. Negative values require

A

to be invertible.

Returns

Tensor

$A^n$ , shape (*, m, m).

Notes

Uses binary exponentiation (repeated squaring) so the cost is $O(\log |n|)$ matrix multiplies rather than $|n|$ . Implemented as a Python composite over matmul and inv so autograd flows naturally — the engine matrix_power_op is not differentiable.

Examples

>>> import lucid
>>> from lucid.linalg import matrix_power
>>> A = lucid.tensor([[1.0, 1.0], [0.0, 1.0]])
>>> matrix_power(A, 5)
Tensor([[1.0000, 5.0000],
        [0.0000, 1.0000]])