quick question on unlocking skills.

If I purchase a skill then make a new character will that skill be unlocked for him even though it didnt say unlocked when I bought it?

Example. I buy earthquake from a skill trainer when its not unlocked. Is it now unlocked for my next character?

When you "unlock" a skill, it's available for any PvP character you make. Also, say you bought earthquake and unlocked it. If you made a new character and got to Lions Arch, you could buy earthquake from the skills guy there because you unlocked it (it might even be sooner, idk)