Two theorems on conditions for nonexistence and for existence, of built functional observers, from an eigenspace perspective are presented and proved. One more theorem on Functional Observability in terms of constructed products of matrices A, C and L-0 is also presented. This theorem provides an easy way to check Functional Observability before proceeding with the design of functional observers. The existence and the nonexistence theorems are used to unify previously reported theorems on Functional Observability by showing their equivalence. The connection between the concept of Functional Observability and the well known concept of State Observability is also presented.