I think I understand now the view matrix well. We have:

objectSpace      →      worldSpace       →      cameraSpace      →       clipSpace         →         NDC space      →       viewportSpace 
           [Model matrix]         [View matrix]         [Projection matrix]    [perspective W division]  …

babaliaris said:
What happens when the forward direction f becomes parallel with the up vector (Looking at the scene from top-down)?

The functions fails on division by zero.

Discussed this recently here: https://www.gamedev.net/forums/topic/707867-lookat-how-to-get-the-correct-temporary-vector-up/​

The…

Why with a cam->vec (0, 1, 0) or (0, -1, 0), a rotation on the yaw axis is actually made on the roll axis ? 
Is it the gimbal lock? It is present only for these two axes? How to fix this problem?