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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.