jax.numpy.linalg.eig

jax.numpy.linalg.eig(a)[source]

Compute the eigenvalues and right eigenvectors of a square array.

LAX-backend implementation of eig().

This differs from numpy.linalg.eig in that the return type of jax.numpy.linalg.eig is always complex64 for 32-bit input, and complex128 for 64-bit input.

Original docstring below.

Parameters

a ((.., M, M) array) – Matrices for which the eigenvalues and right eigenvectors will be computed

Returns

  • w ((…, M) array) – The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be of complex type, unless the imaginary part is zero in which case it will be cast to a real type. When a is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs

  • v ((…, M, M) array) – The normalized (unit “length”) eigenvectors, such that the column v[:,i] is the eigenvector corresponding to the eigenvalue w[i].

References

G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, Various pp.