WebApr 28, 2024 · There are lots of articles, all over the place about the distinction between covariant vectors and contravariant vectors - after struggling through many of them, I … In physics, the principle of covariance emphasizes the formulation of physical laws using only those physical quantities the measurements of which the observers in different frames of reference could unambiguously correlate. Mathematically, the physical quantities must transform covariantly, that is, under a certain representation of the group of coordinate transformations between admissible frames of reference …
Covariant vs contravariant vectors - Physics Stack Exchange
In the field of physics, the adjective covariant is often used informally as a synonym for invariant. For example, the Schrödinger equation does not keep its written form under the coordinate transformations of special relativity. Thus, a physicist might say that the Schrödinger equation is not covariant. In contrast, the … See more In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a See more The general formulation of covariance and contravariance refer to how the components of a coordinate vector transform under a change of basis (passive transformation). … See more In a finite-dimensional vector space V over a field K with a symmetric bilinear form g : V × V → K (which may be referred to as the metric tensor), … See more In category theory, there are covariant functors and contravariant functors. The assignment of the dual space to a vector space is a standard example of a contravariant functor. Some constructions of multilinear algebra are of "mixed" variance, which … See more In physics, a vector typically arises as the outcome of a measurement or series of measurements, and is represented as a list (or See more The choice of basis f on the vector space V defines uniquely a set of coordinate functions on V, by means of $${\displaystyle x^{i}[\mathbf {f} ](v)=v^{i}[\mathbf {f} ].}$$ The coordinates on V are therefore contravariant in the … See more The distinction between covariance and contravariance is particularly important for computations with tensors, which often have mixed … See more WebSep 28, 2024 · What does covariant mean in physics? January 16, 2024 September 28, 2024 by George Jackson. n. The principle that the laws of physics have the same form regardless of the system of coordinates in which they are … jpqrコード決済
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WebAug 8, 2024 · One part are ordinary vector spaces (contravariant), the other dual vector spaces (covariant). Physicists use it this way, the terms contravariant and covariant in mathematics are defined for functors and not for tensors. Furthermore a contravariant functor refers to the dual category, which is exactly the opposite of how physicists use it. WebMar 20, 2012 · The covariant derivative describes the gradient of a vector field (i.e., the effect of applying the gradient vector operator) to the vector, and properly includes the partial derivatives along the coordinate directions of both the vector components and the coordinate basis vectors. Mar 15, 2012. #5. pervect. WebNov 9, 2024 · 1 Answer. The two terms invariant and covariant have different, though somewhat similar meaning. Invariant: Any physical quantity is invariant when its value … jpqr デメリット