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


linalg_eigvalsh(A, UPLO = "L")



(Tensor): tensor of shape (*, n, n) where * is zero or more batch dimensions consisting of symmetric or Hermitian matrices.


('L', 'U', optional): controls whether to use the upper or lower triangular part of A in the computations. Default: 'L'.


A real-valued tensor cointaining the eigenvalues even when A is complex. The eigenvalues are returned in ascending order.


p(λ)=det(AλIn)λR p(\lambda) = \operatorname{det}(A - \lambda \mathrm{I}_n)\mathrlap{\qquad \lambda \in \mathbb{R}}

where is the n-dimensional identity matrix.

The eigenvalues of a real symmetric or complex Hermitian matrix are always real. 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. The eigenvalues are returned in ascending order.

A is assumed to be Hermitian (resp. symmetric), but this is not checked internally, instead:

  • If UPLO\ = 'L' (default), only the lower triangular part of the matrix is used in the computation.

  • If UPLO\ = 'U', only the upper triangular part of the matrix is used.


if (torch_is_installed()) {
a <- torch_randn(2, 2)
#> torch_tensor
#> -1.1600
#>  0.5052
#> [ CPUFloatType{2} ]