Normal (mathematics)

From Wikipedia, the free encyclopedia

In mathematics, normal can have several meanings:

• Surface normal, a vector (or line) that is perpendicular to a surface.
• Normal component, the component of a vector that is perpendicular to a surface.
  • Normal curvature, of a curve on a surface, the component of curvature that is normal to the 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 equations, for linear least squares, a model fitting technique using projection matrices.
• 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 ring, a ring that is its own integral closure in its field of fractions.
• 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.
• Normal polytope, a lattice polytope in which dilation of points is given by summing lattice points.
• Normal measure, a particular type of measure on a measurable cardinal.

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.