[1] Examples of scalar quantities are length, mass, charge, volume, and time.
[2] Scalars are unaffected by changes to a vector space basis (i.e., a coordinate rotation) but may be affected by translations (as in relative speed).
As the vector space in this example and usual cases in physics is defined over the mathematical field of real numbers or complex numbers, the magnitude is also an element of the field, so it is mathematically a scalar.
Since the inner product is independent of any vector space basis, the electric field magnitude is also physically a scalar.
Other examples of scalar quantities are mass, charge, volume, time, speed,[2] pressure, and electric potential at a point inside a medium.
In the theory of relativity, one considers changes of coordinate systems that trade space for time.