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# torch.linalg.eigvals

torch.linalg.eigvals(A, *, out=None) → Tensor

  Computes the eigenvalues of a square matrix.

  Letting K\mathbb{K}K be R\mathbb{R}R or C\mathbb{C}C, the eigenvalues of a square matrix A∈K n×n A \in \mathbb{K}^{n \times n}A∈K n×n are defined as the roots (counted with multiplicity) of the polynomial p of degree n given by

  p(λ)=det⁡(A−λ I n)λ∈C p(\lambda) = \operatorname{det}(A - \lambda \mathrm{I}_n)\mathrlap{\qquad \lambda \in \mathbb{C}}p(λ)=det(A−λ I n​)λ∈C

  where I n\mathrm{I}_n I n​ 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.

  Note

  When inputs are on a CUDA device, this function synchronizes that device with the CPU.

  See also

  `torch.linalg.eig()` computes the full eigenvalue decomposition.

  Parameters:

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

  Keyword Arguments:

    out (Tensor, optional) – output tensor. Ignored if None. Default: None.

  Returns:

    A complex-valued tensor containing the eigenvalues even when `A` is real.

  Examples:

      >>> A = torch.randn(2, 2, dtype=torch.complex128)
      >>> L = torch.linalg.eigvals(A)
      >>> L
      tensor([ 1.1226+0.5738j, -0.7537-0.1286j], dtype=torch.complex128)

      >>> torch.dist(L, torch.linalg.eig(A).eigenvalues)
      tensor(2.4576e-07)

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