I have a question regarding quaternions and rotations.

Let the quaternion q(w, x, y, z) represent the orientation of a camera in world space. I use a UVN camera system where u = right vector, v = up vector and n = forward vector. With zero rotation the camera aligns with the world basis vectors (x, y, z) like so:

u aligns with +x

v aligns with +z

n aligns with +y

My question is how do I construct a quaternion that rotates objects from the RH coordinate system of the world space to a LH coordinate system with the following alignments:

u aligns with +x

v aligns with +y

n aligns with +z

Previously I've use the matrix

[ ux vx nx ]

[ uy vy ny ]

[ uz vz nz ]

however want to switch to a completely quaternion based system.

I suspect I'll need q-1. This rotates objects into camera space, preserving handedness. To switch alignments I suspect I'll need to swap terms in the quaternion.

Thanks.