Normal (mathematics)

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In mathematics, normal can have several meanings:

Surface normal, a line that is perpendicular to a surface
Normal distribution, a type of probability distribution in probability theory and statistics
Normal extension, in abstract algebra, a certain type of algebraic field extensions
Normal family, a pre-compact family of holomorphic functions
Normal function, a continuous strictly increasing function from ordinals to ordinals
Normal matrix, a matrix which commutes with its conjugate transpose
Normal mode, a special type of solution in an oscillating system
Normal morphism, is a morphism that arises as the kernel or cokernel of some other morphisms
Normal number (computing), a number that is within the normal range of a floating-point format
Normal number, a number whose digit sequence is random
Normal operator, a linear operator on a Hilbert space that commutes with its adjoint
Normal space, a topological space in which disjoint closed sets can be separated by disjoint neighborhoods
Normal subgroup, a subgroup that is invariant under conjugation in abstract algebra

Some closely related terms are

Normalizing constant, a constant which scales a mathematical object so that its "size" is equal to one
Unit vector, a vector which has been scaled in such a manner
Orthonormality: two vectors are said to be orthonormal if they are both orthogonal to each other and unit vectors.

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