2024年12月17日 · Topology of Vector Spaces. A topological vector space is a vector space with a compatible topological structure, e.g. induced by a metric. Compatibility means that scalar multiplication and vector addition are continuous functions. This implies that the underlying scalar field is a topological field.

2015年9月1日 · Prove Vector Quadruple Product with Levi-Civita/Index Notation. Oct 7, 2021; Replies 14 Views 12K.

6 天之前 · By experience, my biggest problem with visualizing vector fields is with scaling: field lines can gets too crammed in one part and nonexistent in other parts, and when I try to plot arrow fields, I get either absurdly long arrows where the field is strong and points or empty space where it …

2013年3月12日 · For instance in a 2 foot=0.6096m diameter circular shape I can fit around 7 hexagonal shapes. Even though the logical answer is around 21 the geometry behind it allows me to comfortably pack 7. The same sort of experiment took place with a 4.64m diamater circlular shape. Mathematically from formulas I can fit 539 of these shapes comfortably.

2013年2月20日 · I also liked it when I realized that some sets functions are a vector space and you can basically think of them as n-tuples (for [itex]n = 2^{\aleph_0}[/itex]). Was the first time I saw that vector spaces don't need to consist of actual points in [itex]\mathbb{R}^k[/itex].

2024年6月14日 · A six-vector is an extension of the traditional four-vector used in relativity, incorporating additional dimensions to represent more complex physical quantities. In the context of Minkowski spacetime, a six-vector can be used to encapsulate both the usual spacetime coordinates and additional degrees of freedom, such as those associated with ...

2012年9月24日 · I've attached the .pdf from which I have questions. After it says "Take the square of the numerator" halfway down the page, there is an equation that lists vector components with hats and arrows at the same time, and the arrow on other vectors. Can someone help explain the difference to me...

2010年1月18日 · If course all vector fields exist. I meant real in the sense of "natural". You can do physics with one simple law for the B field, but difficulties in the numerical solution. Or you can do physics with complicating relations between B and H field, but easier numerics. Nature doesn't care if the "numerical" solution is difficult or not.

2021年12月9日 · It is the direction the surface is tilted toward at that (infinitesimal) position. It is usually specified by the direction of the vector normal to the surface at that point. That normal vector is handy in cases like this because it is the direction of the force due to the pressure, ignoring the surface drag.

2020年1月29日 · I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant. I recently watched a video by PBS infinite series...