public Matrix <T> ChangeToThisBasisMatrix(VectorSpace <T> other)
{
Matrix <T> fromBasisMatrix = new Matrix <T>();
Matrix <T> toBasisMatrix = new Matrix <T>();
if (other.basis.Length != basis.Length)
{
throw new ArgumentException("The two vector spaces must be of the same dimension.");
}
for (int i = 0; i < basis.Length; i++)
{
if (!IsVectorInSpace(other.basis[i]) || !other.IsVectorInSpace(basis[i]))
{
throw new ArgumentException("A change of basis matrix can only be created for two equivalent vector spaces.");
}
}
foreach (Vector <T> vec in other.basis)
{
fromBasisMatrix.AppendColumnVector(vec);
}
foreach (IMatrixOperation <T> op in toBasisMatrix.ReducedEchelonFormReductionOperations)
{
op.ApplyTo(fromBasisMatrix);
}
return(fromBasisMatrix);
}
public Matrix <T> ChangeFromThisBasisMatrix(VectorSpace <T> other)
{
return(other.ChangeToThisBasisMatrix(this));
}