What does the ' mean next to this vector?

Question

I am reading through Shankar's Quantum Mechanics and in the first chapter I came across the notation $|0'\rangle$. I am somewhat new to linear algebra (I just learned the basics this past month and I am self-taught, so my understanding is not perhaps as broad as it would be if I'd taken a class. So anyway, I have no idea what the $'$ means, and I'd appreciate any help with that.

Thanks!

Answer 1

If you are referring to the $|0'\rangle$ that appears on page $2$, it's just another vector of the vector space. The notation $0$ is used to emphasize that we want this vector to behave exactly as the zero vector, and the $'$ is because it is, in principle, different to $|0\rangle$. But it turns out that there is exactly one zero vector, so $|0'\rangle$ is indeed $|0\rangle$.

Answer 2

$|0\rangle$ is a null vector. On page 2, $|0'\rangle$ is used to denote another (assumed) null vector in order to define it equal to the first null vector, thus implying the null vector is unique.