I know what you said about pendants but… Apples are integers
Comment on Vectors Part 2
WolfLink@sh.itjust.works 1 week agoA vector space is when you can:
- add two Things
- multiply a Thing by any real number
And get another Thing that’s the same Kind of Thing.
By Thing I mean Vector and by Kind of Thing I mean element of the same Vector Space.
Examples of vector spaces:
- real numbers
- complex numbers
- sets of N numbers (what most people think of when they hear “vector”)
- matrices
- polynomials
- functions
- quantum states of a given system
- quantities of apples sold, classified by type of apple
Examples of Not Vector Spaces:
- integers
- negative numbers
- nonzero numbers
- unitary matrices
- apples
Yeah a few of these come with asterisks I’m happy to answer questions but don’t want to argue with pedants.
porous_grey_matter@lemmy.ml 1 week ago
Hadriscus@lemm.ee 1 week ago
wow didn’t expect this to be so general. How do integers not fit into the definition ? you can add them together and obtain another integer
someacnt_@lemmy.world 1 week ago
When talking about vector space, you usually need the “scalar (field)”, and scalars need inverse to be well-defined.
So for integers, the scalar should be integer itself. Sadly, inverse of integers stops being an integer,
from where all sorts of number theoretic nightmare occursInstead, integers form a ring, and is a module over scalar of integers.