# Normal

From Example Problems

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.