In differential geometry, an isotropic vector field is a concept that refers to a vector field that maintains the same properties in all directions at...

In mathematics, given a vector space X with an associated quadratic form q, written (X, q), a null vector or isotropic vector is a non-zero element x...

isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is an isotropic line. Isotropic coordinates...

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Otherwise it...

wave. The term isotropic radiation means a radiation field which has the same intensity in all directions at each point; thus an isotropic radiator does...

The Lie algebra of Killing vector fields of a spherically symmetric static spacetime takes the same form in the isotropic chart as in the Schwarzschild...

electric field between atoms is the force responsible for chemical bonding that result in molecules. The electric field is defined as a vector field that...

In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle...

electromagnetic (EM) waves in an isotropic medium (that is, a medium whose properties are independent of direction), the electric field vectors (E and D) are in one...

In physics, the electric displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations. It...

letters represent vectors and E is the electric field vector; H is the magnetic field's auxiliary field vector or magnetizing field. This expression is...

fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position...

one-dimensional, spanned by a unit vector u. Since W′ is isotropic, multiplication of elements of W′ inside Cℓ(V, g) is skew. Hence vectors in W′ anti-commute, and...

differential equations, the symplectic form should allow one to obtain a vector field describing the flow of the system from the differential d H {\displaystyle...

This tensor describes a vacuum state with an energy density ρvac and isotropic pressure pvac that are fixed constants and given by ρ v a c = − p v a...

linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation...

the wavefront. In isotropic media, this is also the direction of wave propagation. A closely related vector is the angular wave vector (or angular wavevector)...

polar vector × polar vector = axial vector axial vector × axial vector = axial vector polar vector × axial vector = polar vector axial vector × polar...

is a non-zero vector v ∈ V such that Q(v) = 0, then Q is an isotropic quadratic form. If Q has the same sign for all non-zero vectors, it is a definite...

for some non-zero vectors of V. An indefinite quadratic form takes on both positive and negative values and is called an isotropic quadratic form. More...

at each distance r is proportional to r2, assuming the fluid is fairly isotropic. As a result, a charge fluctuation at any one point has non-negligible...

definite if q(v) < 0) for every nonzero vector v. When q(v) assumes both positive and negative values, q is an isotropic quadratic form. The theorems of Jacobi...

depend on the stress state and velocity of the flow. If the fluid is also isotropic (i.e., its mechanical properties are the same along any direction), the...

loop and the (vector) area of the loop. Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best...

magnetic field is a solenoidal vector field. The Maxwell–Faraday version of Faraday's law of induction describes how a time-varying magnetic field corresponds...

perfect isotropic absorption properties of graphene, the generated solitons could be regarded as vector solitons. How the evolution of vector soliton...

hysteresis loops. The original Jiles–Atherton model is suitable only for isotropic materials. However, an extension of this model presented by Ramesh et...

field. In general, the stress T that a particle P applies on another particle Q across a surface S can have any direction relative to S. The vector T...

In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale...

electric field and the magnetic field lie in the xy-plane. The electric field points in a specific direction in space since it is a vector. The direction...