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An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics.
If a standard score is applied to the ROC curve, the curve will be transformed into a straight line. [50] This z-score is based on a normal distribution with a mean of zero and a standard deviation of one. In memory strength theory, one must assume that the zROC is not only linear, but has a slope of 1.0. The normal distributions of targets ...
In Hamiltonian mechanics, the Boltzmann equation is often written more generally as ^ [] = [], where L is the Liouville operator (there is an inconsistent definition between the Liouville operator as defined here and the one in the article linked) describing the evolution of a phase space volume and C is the collision operator.
The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys ...
In quantum mechanics, energy is defined in terms of the energy operator, acting on the wave function of the system as a consequence of time translation symmetry. Definition [ edit ]
summation operator area charge density: coulomb per square meter (C/m 2) electrical conductivity: siemens per meter (S/m) normal stress: pascal (Pa) scattering cross section: barn (10^-28 m^2) surface tension: newton per meter (N/m) tau: torque: newton meter (N⋅m) shear stress: pascal time constant: second (s) 6.28318...
In general, any operator in a Hilbert space that acts by permuting an orthonormal basis is unitary. In the finite dimensional case, such operators are the permutation matrices. On the vector space C of complex numbers, multiplication by a number of absolute value 1, that is, a number of the form e iθ for θ ∈ R, is a unitary operator.
In special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator [1] (cf. nabla symbol ) is the Laplace operator of Minkowski space .