WebMar 24, 2024 · A covariant tensor, denoted with a lowered index (e.g., ) is a tensor having specific transformation properties. In general, these transformation properties differ from … WebCovariant and contravariant bases are dual to one another and are physics nomenclature for constructs that arise in differential geometry. The problem here is that physicists often need to use differential geometry (for example, for relativity) long before they have seen a proper course on differential geometry.
Chapter 10 Vectors and Tensors - gatech.edu
WebMay 31, 2024 · In the sense that it is defined using the upper indices (i.e. the contravariant form). And it has the corresponding dual or co-vector . The four-velocity is then defined … A covariant vector or cotangent vector (often abbreviated as covector) has components that co-vary with a change of basis. That is, the components must be transformed by the same matrix as the change of basis matrix. The components of covectors (as opposed to those of vectors) are said to be covariant. 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), there is little distinction between covariant and contravariant vectors, because the bilinear form allows covectors to be … See more The distinction between covariance and contravariance is particularly important for computations with tensors, which often have mixed variance. This means that they have both covariant and contravariant components, or both vector and covector components. The … 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 tuple) of numbers such as $${\displaystyle (v_{1},v_{2},v_{3}).}$$ The numbers in the list depend on the choice of See more The choice of basis f on the vector space V defines uniquely a set of coordinate functions on V, by means of The coordinates on … See more 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 … See more barker at barker 1993 wika
19.6: Appendix - Tensor Algebra - Physics LibreTexts
Webcomponents are identi ed with superscripts like V , and covariant vector components are identi ed with subscripts like V . The mnemonic is: \Co- is low and that’s all you need to … WebMar 24, 2024 · A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor ). To examine the transformation properties of a contravariant tensor, first consider a tensor of rank 1 (a vector ) (1) for which (2) Now let , then any set of quantities which transform according to (3) or, defining (4) according to (5) barker arkansas