public static bool LinearlyDependent(Vector <Real>[] vectors)
{
if (vectors.Select(v => v.Dimension).Distinct().Count() > 1)
{
throw new IncompatibleOperationException(VectorOperationType.Dimension);
}
// If the amount of vectors is greater than the dimension they're
// automatically linearly dependent.
if (vectors[0].Dimension < vectors.Length)
{
return(true);
}
var m = new RealMatrix(vectors);
if (m.IsSquare())
{
return(m.Determinant().Equals(0));
}
m = m.ToReducedEchelonForm().ToRealMatrix();
return(m.AmountOfNullRows() != 0);
}
/// <summary>
/// Gets the eigenvalues of the given matrix, calculated numerically from the
/// characteristic polynomial of this matrix. Continues until all eigenvalues
/// have been found.
/// </summary>
/// <param name="m"></param>
/// <returns></returns>
public static RealVector RealEigenValues(this RealMatrix m)
{
if (!m.IsSquare())
{
throw new IncompatibleOperationException(MatrixOperationType.Eigenvalue);
}
ComplexVector values = new ComplexVector(m.Width);
throw new NotImplementedException();
}
