using System;

namespace Science.Mathematics.LinearAlgebra
{
    public class Subspace : VectorSpace
    {
        public Subspace(int dimension) : base(dimension)
        {
        }
        public Subspace(Vector[] basis) : base(basis)
        {
            this.Basis = basis;
            this.Dimension = basis.Length;
        }
        public Subspace(Matrix basis)
        {
            Vector[] v = new Vector[basis.SizeOfColumn];
            for (int i = 0; i < v.Length; i++)
            {
                v[i] = new Vector(basis.SizeOfRow);
                for (int j = 0; j < basis.SizeOfRow; j++)
                    v[i][j] = basis[j, i];  
            }
            this.Basis = v;
            this.Dimension = v.Length;
        }
        public bool IsInSpaceQ(Vector v)
        {
            Projection obj = new Projection(this, v);
            if (obj.Error.Norm < 1.0E-12) return true;
            else return false;
        }
    }
}