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A normal vector of length one is called a unit normal vector. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by −1 results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior).
In general, the value of the norm is dependent on the spectrum of : For a vector with a Euclidean norm of one, the value of ‖ ‖ is bounded from below and above by the smallest and largest absolute eigenvalues of respectively, where the bounds are achieved if coincides with the corresponding (normalized) eigenvectors.
A real random vector = (, …,) is called a centered normal random vector if there exists a matrix such that has the same distribution as where is a standard normal random vector with components. [ 1 ] : p. 454
Feature scaling is a method used to normalize the range of independent variables or features of data. In data processing , it is also known as data normalization and is generally performed during the data preprocessing step.
All these extensions are also called normal or Gaussian laws, so a certain ambiguity in names exists. The multivariate normal distribution describes the Gaussian law in the k-dimensional Euclidean space. A vector X ∈ R k is multivariate-normally distributed if any linear combination of its components Σ k j=1 a j X j has a (univariate) normal ...
Normalizing constant, in probability theory a constant to make a non-negative function a probability density function; Noether normalization lemma, the result of commutative algebra; Vector normalization; Normalized number, a number in scientific notation with the decimal point in a consistent position; Probability amplitude § Normalization
A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The term normalized vector is sometimes used as a synonym for unit vector. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
Illustration of tangential and normal components of a vector to a surface. In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector.