eigenvalues method

@override List<Complex> eigenvalues()

Returns the eigenvalues associated to this matrix.

Eigenvalues can only be computed if the matrix is square, meaning that it must have the same number of columns and rows.

Implementation

@override
List<Complex> eigenvalues() {
  if (!isSquareMatrix) {
    throw const MatrixException(
      'Eigenvalues can be computed on square matrices only!',
    );
  }

  // From now on, we're sure that the matrix is square. If it's 1x1 or 2x2,
  // computing the roots of the characteristic polynomial is faster and more
  // precise.
  if (rowCount == 1 || rowCount == 2) {
    return characteristicPolynomial().solutions();
  }

  // For 3x3 matrices and bigger, use the "eigendecomposition" algorithm.
  final eigenDecomposition = EigendecompositionComplex(
    matrix: this,
  );

  // The 'D' matrix contains real and complex coefficients of the eigenvalues
  // so we can ignore the other 2.
  final decomposition = eigenDecomposition.decompose()[1];
  final eigenvalues = <Complex>[];

  for (var i = 0; i < decomposition.rowCount; ++i) {
    eigenvalues.add(decomposition(i, i));
  }

  return eigenvalues;
}