# Unobservable states

• Engineering
pj33
Homework Statement:
Why the null space of the Observable matrix is not the same as the state vector?
Relevant Equations:
None
https://en.wikipedia.org/wiki/Observability

I am studying observability and I try to get some intuition on the topic.
Given the observable matrix, we can find the null space. However, the vectors of the null space are states but this differs from the definition of what a state vector of a system is. In addition, the null space indicates that all the states with the same velocity are indistinguishable. Why is this the case ?

Why is that?
Is it because the state vector is a vector containing other vectors (position velocity etc), that's why it differs from the state in the null space.