det

→Tensor

det(x: Tensor)

source

Compute the determinant of a square matrix.

For a square matrix $A \in \mathbb{R}^{n \times n}$ returns the scalar $\det(A)$ . The determinant is the signed volume of the parallelepiped spanned by the rows (or columns) of $A$ ; it is non-zero if and only if $A$ is invertible.

Parameters

xTensor

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

Returns

Tensor

Determinant of shape (*,) (one scalar per batch entry).

Notes

Computed as the product of the diagonal of $U$ from $PA = LU$ together with the sign of the row-permutation $P$ . Cost is $O(n^3)$ .

For numerically large matrices $\det(A)$ can overflow or underflow easily — prefer slogdet which returns $(\mathrm{sign},\,\log|\det A|)$ and is stable across scales.

Examples

>>> import lucid
>>> from lucid.linalg import det
>>> det(lucid.tensor([[1.0, 2.0], [3.0, 4.0]]))
Tensor(-2.0)