(5,3)-Jection Operator in Hilbert Space

We study (5,3) - Jections in context of a Hilbert Space. In space R2, we investigate different forms of E(x,y) such that E(x, y) is a (5,3) - Jection. We also study cases when it is also a positive operator. We show that when product of two (5,3)- Jection is zero, then the sum is also a (5,3)- Jection. We also see that the set of all mutually orthogonal (5,3)- Jection form an abelian group with respect to addition. We show that if T1, T2 are commuting (5,3)- Jection then the product is also a (5,3)- Jection except some exceptions in Hilbert Space R2.