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.

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