Eigenvalue Problems

Methods

======================================= ============ Method Description ======================================= ============ eig_ (A) Eigenvalue and eigenvectors eigvals_ (A) Eigenvalues eigh_ (A[, eigvals_only]) Eigenvalue and eigenvectors for hermitian/symmetric matrix eigvalsh_ (A) Eigenvalues for hermitian/symmetric matrix eigBanded_ (A[, eigvals_only]) Eigenvalue and eigenvectors for banded matrix eigvalsBanded_ (A) Eigenvalues for banded matrix eighTridiagonal_ (d, e[, eigvals_only]) Eigenvalue and eigenvectors for tridiagonal matrix eigvalshTridiagonal_ (d, e) Eigenvalues for tridiagonal matrix ======================================= ============

Description

.. _eig:

.. function:: eig(A[, right])

:param A: Matrix<Float64>
:param right: Bool, whether to find right or left eigenvectors. Default to true.
:return: (Vector<Complex64>, Matrix<Complex64>)

.. function:: eig(A[, right])

:param A: Matrix<Float32>
:param right: Bool, whether to find right or left eigenvectors. Default to true.
:return: (Vector<Complex32>, Matrix<Complex32>)

.. function:: eig(A[, right])

:param A: Matrix<Complex64>
:param right: Bool, whether to find right or left eigenvectors. Default to true.
:return: (Vector<Complex64>, Matrix<Complex64>)

.. function:: eig(A[, right])

:param A: Matrix<Complex32>
:param right: Bool, whether to find right or left eigenvectors. Default to true.
:return: (Vector<Complex32>, Matrix<Complex32>)

Compute eigenvalues and eigenvectors of a matrix.

.. _eigvals:

.. function:: eigvals(A)

:param A: Matrix<Float64>
:return: Vector<Complex64>

.. function:: eigvals(A)

:param A: Matrix<Float32>
:return: Vector<Complex32>

.. function:: eigvals(A)

:param A: Matrix<Complex64>
:return: Vector<Complex64>

.. function:: eigvals(A)

:param A: Matrix<Complex32>
:return: Vector<Complex32>

Compute eigenvalues of a matrix.

.. _eigh:

.. function:: eigh(A[, eigvals_only])

:param A: Matrix<Float64>
:param eigvals_only: Bool, default to false
:return: (Vector<Float64>, Matrix<Float64>)

Compute the eigenvectors and eigenvalues of a symmetric/hermitian matrix.

**Note.** Currently only the real version is implemented.

.. _eigvalsh:

.. function:: eigvalsh(A)

:param A: Matrix<Float64>
:return: Vector<Float64>

Compute the eigenvalues of a symmetric/hermitian matrix.

**Note.** Currently only the real version is implemented.

.. _eigBanded:

.. function:: eigBanded(A[, eigvals_only])

:param A: Matrix<Float64>
:param eigvals_only: Bool, default to false
:return: (Vector<Float64>, Matrix<Float64>)

Compute the eigenvectors and eigenvalues of a banded matrix.

.. _eigvalsBanded:

.. function:: eigvalsBanded(A)

:param a: Matrix<Float64>
:return: Vector<Float64>

Compute the eigenvalues of a banded matrix.

.. _eighTridiagonal:

.. function:: eighTridiagonal(d, e[, eigvals_only])

:param d: Vector<Float64>
:param e: Vector<Float64>
:param eigvals_only: Bool, default to false
:return: (Vector<Float64>, Matrix<Float64>)

Compute the eigenvectors and eigenvalues of a tridiagonal matrix.

.. _eigvalshTridiagonal:

.. function:: eigvalshTridiagonal(d, e)

:param d: Vector<Float64>
:param e: Vector<Float64>
:return: Vector<Float64>

Compute the eigenvalues of a tridiagonal matrix.