Prolixity | A programming language designed for iOS devices | iOS library

Your basic understand of the camera and view matrix is correct. The camera is normally used to describe the position and orientation of the viewer/camera in the world while the view matrix would be used to transform from world space to view space so it should be the inverse of the camera matrix.

Note that in matrix math there is a difference in the order in which transformations are applied: rotating and then translating is different from translating and then rotating (we'll leave scaling out of the equation here since you normally don't scale a camera - zooming would be done via the projection matrix).

When building your camera matrix you'd first rotate to set camera orientation and then translate to set camera position, i.e. you treat the camera as sitting at 0/0/0, looking along the z axis (so the view vector would be 0/0/1). After rotating you get a different normalized view vector but the camera would still "sit" at 0/0/0. Then you translate to the actual camera position (you might need additional matrix operations to calculate that position but I'd do that in a separate step for starters - until you get things right).

Can you explain me how first rotating and then translating with the negative camera position provides the inverted camera transformation matrix please?

It shouldn't as the resulting view matrix would apply a different direction. The "negative" rotation (i.e. angle +/- 180 degrees) should work though. In that case you rotate a vector to point to the camera (so if the camera turns 45 degrees around the y-axis any object "pointing to the camera" would need to rotate by 225 or -135 degrees around the same axis).

Negative translation is ok since if you move the camera to 4/3/2 in world space a translation by -4/-3/-2 would move any coordinate in world space into view space.