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In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space. [1] A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane.
A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar, a vector, a spinor, or a tensor, respectively. A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field ...
Muladhara Chakra (मूलाधार चक्र) Muladhara (Sanskrit: मूलाधार or मूलाधारा; IAST: Mūlādhāra, lit. "root of Existence." Mula means root and dhara means flux.) or the root chakra is one of the seven primary chakras according to Hindu tantrism. It is symbolized by a lotus with four petals and ...
In physics, a vector field (,,) is a function that returns a vector and is defined for each point (with coordinates ,,) in a region of space. The idea of sources and sinks applies to b {\displaystyle \mathbf {b} } if it follows a continuity equation of the form
If F is a subfield of E then E is an extension field of F. We then also say that E/F is a field extension. Degree of an extension Given an extension E/F, the field E can be considered as a vector space over the field F, and the dimension of this vector space is the degree of the extension, denoted by [E : F]. Finite extension
In the study of mathematics, and especially of differential geometry, fundamental vector fields are instruments that describe the infinitesimal behaviour of a smooth Lie group action on a smooth manifold. Such vector fields find important applications in the study of Lie theory, symplectic geometry, and the study of Hamiltonian group actions.
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Vector field (right) and corresponding scalar potential (left). A scalar potential is a fundamental concept in vector analysis and physics (the adjective scalar is frequently omitted if there is no danger of confusion with vector potential). The scalar potential is an example of a scalar field.