Computes the eigenvalues of a square matrix.

Letting be or , the eigenvalues of a square matrix are defined as the roots (counted with multiplicity) of the polynomial p of degree n given by

Usage

linalg_eigvals(A)

Arguments

A: (Tensor): tensor of shape (*, n, n) where * is zero or more batch dimensions.

Details

$p(\lambda) = \operatorname{det}(A - \lambda \mathrm{I}_n)\mathrlap{\qquad \lambda \in \mathbb{C}}$

where is the n-dimensional identity matrix. 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.

Note

The eigenvalues of a real matrix may be complex, as the roots of a real polynomial may be complex. The eigenvalues of a matrix are always well-defined, even when the matrix is not diagonalizable.

Other linalg: linalg_cholesky(), linalg_cholesky_ex(), linalg_det(), linalg_eig(), linalg_eigh(), linalg_eigvalsh(), linalg_householder_product(), linalg_inv(), linalg_inv_ex(), linalg_lstsq(), linalg_matrix_norm(), linalg_matrix_power(), linalg_matrix_rank(), linalg_multi_dot(), linalg_norm(), linalg_pinv(), linalg_qr(), linalg_slogdet(), linalg_solve(), linalg_solve_triangular(), linalg_svd(), linalg_svdvals(), linalg_tensorinv(), linalg_tensorsolve(), linalg_vector_norm()

Examples

if (torch_is_installed()) {
a <- torch_randn(2, 2)
w <- linalg_eigvals(a)
}