joppy

44 ms·

421.
by joppy 8y ago
Since the quaternion norm is induced via the quaternion dot product, any transformation that preserves the norm automatically also preserves the dot product. This is a standard result for inner product spaces.
422.
by joppy 8y ago
Unitary in what sense? Clearly multiplication by a unit quaternion preserves the quaternion norm.
423.
by joppy 8y ago
I don’t really understand the main argument given in the article; since zero has no multiplicative inverse, you can’t prove anything involving a division by zero. (So why talk about field axioms?) However, to extend an operation usefully to
424.
by joppy 8y ago
I don’t think 1/0 = infinity is a good choice either, since -1/0 = 1/(-1 * 0) = 1/0, so we would have infinity being equal to negative infinity, which is assumedly not a practical choice. 1/0 = 0 is actually more sy
425.
by joppy 8y ago
Why infinity rather than negative infinity? Is 1/0 = 1/(-0)?
426.
by joppy 8y ago
There is a process where you put in a space (number of dimensions) and a metric (Euclidean, for example) and produce a Clifford algebra. This is also sometimes called “geometric algebra”, although there are a lot of sensationalist posts usi
427.
by joppy 8y ago
Making the plane infinite makes the problem easier, since you don’t need to worry about the boundary of any finite section of the plane. For example, if you choose a triangular section, you won’t be able to tile that section by squares. Bu
428.
by joppy 8y ago
Defer is for reclaiming resources, or other cleanup at the end of a function which cannot otherwise be handled by the language, and (usually?) this is not going to be in your hot path; for example opening and closing a file many many times
429.
by joppy 8y ago
If you are using the Opera browser on Android, then when you zoom, the text resizes but then reflows to fit on the screen. I cannot fathom why the other phone browsers do not have this feature, it makes every site readable without any scrol
430.
by joppy 9y ago
I don't think that octonions are the obvious next step here. They are a non-associative algebra, and therefore incredibly difficult to deal with. Starting with real n-space, one can form the Clifford algebra, which essentially gives a
431.
by joppy 9y ago
A field is algebraically closed if whenever you have a polynomial with coefficients in that field, all the roots of the polynomial also belong to the field. For example: The field of rational numbers is not closed since it does not contain
432.
by joppy 9y ago
In the case where the base ring R is a field (all of typical linear algebra), then the space associated to it is a point. So a vector bundle over this point is just a vector space, so we didn't really gain any extra geometry here - if
433.
by joppy 9y ago
The author was trying to analyse the effect of loaded dice on a game of Catan, not test whether the water-soaking method produced loaded dice. It doesn't really matter where the loaded dice came from.
434.
by joppy 9y ago
Why should all mathematics be written using exactly the same language and conventions? Should all computer programs be written in the same language? People modify the language (natural, mathematical, programming) they are using to suit thei