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 …
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 …
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 · I've just learned about contra- and covariant vector in the context of special relativity (in electrodynamic) and I'm struggling with some concept. From what I found, an intuitive definition of
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 …
general relativity - Contravariant vectors in physics relation to ...
Feb 17, 2025 · 2. Vectors in Physics (e.g., in Special Relativity) In physics, a contravariant vector $ x^\mu $ (like position or velocity) is simply an object that transforms under a change of coordinates …
Is it foolish to distinguish between covariant and contravariant vectors?
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 …
Covariant and contravariant components of a vector in curvilinear ...
Dec 25, 2019 · I'm reading a Quora answer on an intuitive explanation of covariant/contravariant components of vectors. If we have a coordinate system with straight coordinate axes, the geometric …
Contravariant - covariant notations - Physics Stack Exchange
Apr 13, 2020 · The reason contravariant and covariant indices have to be contracted together and not contravariant-contravariant or covariant-covariant contraction is because in the context of physics …