{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "",
              "annotation": "LinAlgError",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If eigenvalue computation does not converge."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "w",
              "annotation": "(M,) or (2, M) double or complex ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The eigenvalues, each repeated according to its multiplicity. The shape is (M,) unless "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "homogeneous_eigvals=True"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "vl",
              "annotation": "(M, M) double or complex ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The left eigenvector corresponding to the eigenvalue "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "w[i]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the column "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "vl[:,i]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". Only returned if "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "left=True"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". The left eigenvector is not normalized."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "vr",
              "annotation": "(M, M) double or complex ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The normalized right eigenvector corresponding to the eigenvalue "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "w[i]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the column "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "vr[:,i]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ".  Only returned if "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "right=True"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Solve an ordinary or generalized eigenvalue problem of a square matrix."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "a",
              "annotation": "(M, M) array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "A complex or real matrix whose eigenvalues and eigenvectors will be computed."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "b",
              "annotation": "(M, M) array_like, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Right-hand side matrix in a generalized eigenvalue problem. Default is None, identity matrix is assumed."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "left",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to calculate and return left eigenvectors.  Default is False."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "right",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to calculate and return right eigenvectors.  Default is True."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "overwrite_a",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to overwrite "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "; may improve performance.  Default is False."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "overwrite_b",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to overwrite "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "; may improve performance.  Default is False."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "check_finite",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "homogeneous_eigvals",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If True, return the eigenvalues in homogeneous coordinates. In this case "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "w"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is a (2, M) array so that      "
                    }
                  ]
                },
                {
                  "__type": "Code",
                  "__tag": 4050,
                  "value": "w[1,i] a vr[:,i] = w[0,i] b vr[:,i]",
                  "execution_status": null
                },
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Default is False."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Find eigenvalues w and right or left eigenvectors of a general matrix      "
            }
          ]
        },
        {
          "__type": "Code",
          "__tag": 4050,
          "value": "a   vr[:,i] = w[i]        b   vr[:,i]\na.H vl[:,i] = w[i].conj() b.H vl[:,i]",
          "execution_status": null
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "where "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": ".H"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the Hermitian conjugation."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The documentation is written assuming array arguments are of specified \"core\" shapes. However, array argument(s) of this function may have additional \"batch\" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "linalg_batch",
              "domain": null,
              "role": "ref",
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for details. Note that calls with zero-size batches are unsupported and will raise a "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "ValueError"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/scipy/linalg/_decomp.py",
  "item_line": 114,
  "item_type": "function",
  "aliases": [
    "scipy.linalg.eig"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\nfrom scipy import linalg\na = np.array([[0., -1.], [1., 0.]])\nlinalg.eigvals(a)\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "b = np.array([[0., 1.], [1., 1.]])\nlinalg.eigvals(a, b)\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "a = np.array([[3., 0., 0.], [0., 8., 0.], [0., 0., 7.]])\nlinalg.eigvals(a, homogeneous_eigvals=True)\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "a = np.array([[0., -1.], [1., 0.]])\nlinalg.eigvals(a) == linalg.eig(a)[0]\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "linalg.eig(a, left=True, right=False)[1] # normalized left eigenvector\nlinalg.eig(a, left=False, right=True)[1] # normalized right eigenvector\n",
        "execution_status": "failure"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "eig_banded",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.linalg._decomp:eig_banded"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "eigenvalues and right eigenvectors for symmetric/Hermitian band matrices"
            }
          ]
        }
      ],
      "type": "func"
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "eigh",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "eigh"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Eigenvalues and right eigenvectors for symmetric/Hermitian arrays."
            }
          ]
        }
      ],
      "type": "func"
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "eigh_tridiagonal",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.linalg._decomp:eigh_tridiagonal"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "eigenvalues and right eigenvectors for symmetric/Hermitian tridiagonal matrices"
            }
          ]
        }
      ],
      "type": "func"
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "eigvals",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.linalg._decomp:eigvals"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "eigenvalues of general arrays"
            }
          ]
        }
      ],
      "type": "func"
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "b",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "left",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "right",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "overwrite_a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "overwrite_b",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "check_finite",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "homogeneous_eigvals",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "eig"
  },
  "references": null,
  "qa": "scipy.linalg._decomp:eig",
  "arbitrary": [],
  "local_refs": [
    "a",
    "b",
    "check_finite",
    "homogeneous_eigvals",
    "left",
    "overwrite_a",
    "overwrite_b",
    "right",
    "vl",
    "vr",
    "w"
  ]
}