Quantum Superposition, Linear Combinations and Basis

[gfghfhghfghfgh]

Hello, just a quick question.

I am aware that a a state in a space can be written as a linear combination of the basis kets of that space

ψ = ∑ai[ψi]

where ai are coefficients and [ψi] are the basis vectors.

I was just wondering is this a linear superposition of states or just a linear combination?

Can it only be a linear superposition if the basis kets are eigenstates of some operator?

Thank you

 

[blue_leaf77]

I was just wondering is this a linear superposition of states or just a linear combination?

I don't know if it's necessary to consider them different. The traditional way is that, say you have two vectors $v_1$ and $v_2$. The linear combination between them is a vector such that $v = a_1v_1 + a_2v_2$ for some scalar $a_1$ and $a_2$. Very strictly speaking, in that equation $v_1$ and $v_2$ do not superpose, instead $a_1v_1$ and $a_2v_2$ do. Do you get the idea now?