of a vector r
, usually written |r
|, or sometimes simply r, is defined to be the length of the vector r
. If r
is written in terms of three orthonormal vectors (ie: mutually perpendicular vectors of unit length), i
- r = xi+yj+zk,
the modulus of r
is the square root
It should be noted that the modulus of a vector is a scalar.
Modulus is also a synonym for:
In materials science
modulus (or elastic modulus) is a measure of the stiffness of a material. See also Young's modulus
In computer programming, the modulus operator gives the remainder of integer division, ie modular arithmetic. Mathematicians tend to call this modulo, for example:
- 13 = 3 modulo 10
- 13 = 3 mod 10
This is because 10 is here the modulus of the congruence
, and modulo
(a Latin ablative) stands for 'to the modulus'.
C programmers will write:
- 13 % 10 = 3.