norm,
n. 1. the length of a vector expressed as the square root of the sum of the squares of its orthogonal components.
2a. a non-negative real-valued function defined on the members of a vector-space, satisfying the conditions that
|| -x || = || x ||,
|| tx || = | t | • || x || for scalar t,
and the triangle inequality
|| x + y || ≤ || x || + || y ||
where || x || is the norm of x.
b. (as a prefix) with respect to a given norm or in the topology induced by a given norm. For example, a norm-convergent or norm-bounded function is convergent or bounded with respect to some norm; a norm-compact function is compact with respect to the norm topology; and a norm-one element has unit norm. 3. an everywhere finite Minkowski function or gauge. 4. (of an algebraic number) the product of all the conjugates to the given number; for example, the norm of an algebraic number of the form a + b√d is a2 - db2 for any integers a, b, and d. 5. another word for mesh-fineness. 6. (Statistics) another term for the mode of a distribution.
2a. a non-negative real-valued function defined on the members of a vector-space, satisfying the conditions that
|| -x || = || x ||,
|| tx || = | t | • || x || for scalar t,
and the triangle inequality
|| x + y || ≤ || x || + || y ||
where || x || is the norm of x.
b. (as a prefix) with respect to a given norm or in the topology induced by a given norm. For example, a norm-convergent or norm-bounded function is convergent or bounded with respect to some norm; a norm-compact function is compact with respect to the norm topology; and a norm-one element has unit norm. 3. an everywhere finite Minkowski function or gauge. 4. (of an algebraic number) the product of all the conjugates to the given number; for example, the norm of an algebraic number of the form a + b√d is a2 - db2 for any integers a, b, and d. 5. another word for mesh-fineness. 6. (Statistics) another term for the mode of a distribution.