what about Covariant and Contravariant transformation of vector. Does it always preserve the length of vector in any coordinate system.

Hi, everybody.

I released a Python library you might like.

github.com/DanielSank/constraintula

@DanielSank 1. I can guess what it does but it would be nice if the readme/documentation told me explicitly ;) 2. Isn't the circle/area constraint dangerous because floating point equality is a horrible minefield?

This almost preserve the length (vary in few values) of vector in skew coordinate system with 1:1 axes ratio.

what do you mean by "coordinate system" for a vector space and what is your definition of "length"?

a metric on a vector space is usually defined to not depend on the choice of basis.

Hello @ACuriousMind "Length" means metric of vector space.

"Coordinate System" means orthogonal / non-orthogonal coordinates.

a vector space doesn't automatically have a metric

@123 vector spaces don't have "coordinates"

coordinates are a concept for manifolds

vector spaces just have different choices of basis

But we can find norm of any vector space?

A "normed space" is a vector space equipped with a "norm"

this might be useful

In other news:

India confirms now 93,000 cases per day. But isn’t testing widely. The true number of new infections is estimated to be up to 800,000 per day.

@JohnRennie My uni does the same for physics

seemingly just a lesser but easier to complete degree