From Wikipedia, the free encyclopedia.
The modulus 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, j and k such that:
- r = xi + yj + zk,
The modulus of a vector is a scalar.
One special case is the absolute value of a complex number, defined to be the distance between the origin and the complex number, thought of as a point in the plane, and in particular the absolute value of a real number.
The word modulus also denotes the number by which two numbers are said to be congruent in modular arithmetic. A related, incorrect use of 'modulus' is for the remainder after integer division (see below).
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
C programmers will write:
- 13 % 10 = 3.
