Most mathematical functions in Mathematica
are set up to apply themselves separately to each element in a list. This is true in particular of all functions that carry the attribute Listable
A consequence is that most mathematical functions are applied element by element to matrices and vectors.
It is important to realize that Mathematica
treats an object as a vector in a particular operation only if the object is explicitly a list at the time when the operation is done. If the object is not explicitly a list, Mathematica
always treats it as a scalar. This means that you can get different results, depending on whether you assign a particular object to be a list before or after you do a particular operation.