As already stated, the answer to the original OP’s question is yes; mounting 100mm FX lens on a DX camera will give you the equivalent angle of view of a 150mm lens.
Some very good explanations have been given but I agree with KISS and “almost gives me a headache”. I may be producing yet another kind of headache
My attempt at simplifying …
Focal length equivalents for DX (APS-C) and FX (full frame) lenses … “crop factor”
ANY FX or DX lens on a DX sensor camera
Equivalent Focal Length = 1.5 X (actual marked focal length). Example: 100mm lens = 150mm equiv. = 1.6 X (actual marked FL for Canon) Example: 100mm lens = 160mm
ANY FX or DX lens on an FX sensor camera, no crop factor
Equivalent Focal Length = actual focal length. Example: 100mm lens = 100mm
ANY lens on a 4/3 sensor camera (micro in micro four thirds, only refers to the lens mount)
Equivalent Focal Length = 2 X (actual marked FL). Example: 100mm lens = 200mm equiv.
Other sensor (and film) sizes have lens view equivalents that can be compared to “full frame” sensors, according to their relative sizes.
So… to judge your field of view, equivalent angle of view, lens does not change...
if using a DX camera, multiply ALL lens FLs by 1.5
If using an FX camera, lens view is what is marked
If using Micro 4/3 cameras, multiply all lens FLs by 2