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A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis.
Normalization property (abstract rewriting), a property of a rewrite system in mathematical logic and theoretical computer science; 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
In relativistic laser-plasma physics the relativistic similarity parameter S is a dimensionless parameter defined as =, where is the electron plasma density, = / is the critical plasma density and = / is the normalized vector potential.
The normalization condition that the trace of be equal to 1 defines the partition function to be () = (). If the number of particles involved in the system is itself not certain, then a grand canonical ensemble can be applied, where the states summed over to make the density matrix are drawn from a Fock space .
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which ...
(Whether the null vector counts as a valid state ("no system present") is a matter of definition. The null vector does not at any rate describe the vacuum state in quantum field theory.) The set of allowable states is a vector space. This similarity is of course not accidental.
Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics.
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,