inv

inv(x: array, /) → array

Returns the multiplicative inverse of a square matrix (or a stack of square matrices) x.

If x is real-valued, let \(\mathbb{K}\) be the set of real numbers \(\mathbb{R}\), and, if x is complex-valued, let \(\mathbb{K}\) be the set of complex numbers \(\mathbb{C}\).

The inverse matrix \(x^{-1} \in\ \mathbb{K}^{n \times n}\) of a square matrix \(x \in\ \mathbb{K}^{n \times n}\) is defined as

\[x^{-1}x = xx^{-1} = I_n\]

where \(I_n\) is the n-dimensional identity matrix.

The inverse matrix exists if and only if x is invertible. When x is invertible, the inverse is unique.

When x is a stack of matrices, the function must compute the inverse for each matrix in the stack.

Parameters:

x (array) – input array having shape (..., M, M) and whose innermost two dimensions form square matrices. Should have a floating-point data type.

Returns:

out (array) – an array containing the multiplicative inverses. The returned array must have a floating-point data type determined by Type Promotion Rules and must have the same shape as x.

Notes

Changed in version 2022.12: Added complex data type support.