Covariant vs contravariant vectors - Physics Stack Exchange
Apr 6, 2020 · Technically contravariant vectors are in one vector space, and covariant vectors are in a different space, the dual space. But there is a clear 1-1 correspondence between the space and its …
Covariant and contravariant for a beginner - Physics Stack Exchange
Oct 27, 2021 · But, I can't get deeper into covariant and contravariant. I even saw some people use an equation like this: $^ia_j$. I was reading Covariant vs contravariant vectors, and those answers don't …
Confusions about Covariant and Contravariant vectors
Oct 22, 2016 · I say "clunky" because saying a vector has "covariant/contravariant components" totally wipes out the geometric interpretations of vectors and covectors, shown in Alfred's answer; it makes …
special relativity - Understanding the difference between co- and ...
Covariant and contravariant vectors can be thought of as different flavors of vectors in physics. Most of the vectors which occur in the usual classical physics like position, velocity etc. are contravariant, …
Covariant and contravariant 4-vector in special relativity
Dec 31, 2015 · Wikipedia with the classical example being the gradient. Now what bothers me is this "lowering and rising index" stuff where one can transform a contravariant vector to a covariant one …
How to visualize the physical examples of contravariant and covariant ...
Dec 7, 2017 · A [contravariant] vector acts on a dual vector to produce a scalar, and the visual picture of this is the number of surfaces the arrow crosses. Some classic textbook on electromagnetism gave a …
general relativity - Is it foolish to distinguish between covariant and ...
So there is actually no difference between a contravariant and covariant vector, there is a difference between a contravariant and covariant basis as is shown in arXiv:1002.3217. An inner product is …
Gradient is covariant or contravariant? - Physics Stack Exchange
Jul 14, 2016 · You can verify that the normal vector has covariant components by recalling that the normal can be defined through a cross product of tangent vectors (which have contravariant …
How to calculate the covariant derivative $\nabla_ {\bf e_\beta} {\bf e ...
However, because of the definition of this derivative, doesn't that mean $\mathbf {e}'_ {\alpha}$ is a vector field? It is hard for me to understand the meaning of "a vector field of basis vectors." Also, …
Geometrical representation of Contravariant and covariant vectors
Jun 16, 2021 · After cruising through a lot of material online, and answers over here, my understanding of contravariant and covariant vectors are, in a finite-dimensional vector space, suppose we have a …