Could you tell me if Quaternion (-Q0, Qx, Qy, Qz) is exactly the same as (Q0,-Qx, -Qy, -Qz)?

I am testing a SW tool against a formula and I have noticed that sometimes the signs are different.

The calculated position of an object in 3D space, from a SW tool, is as follows:
Quaternion (-Q0, Qx, Qy, Qz)
From a formula, I obtained:
(Q0,-Qx, -Qy, -Qz)