Vector space bijection #17
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Here's a preview of the resulting doc: https://github.com/llewelld/hut23-linear-algebra/blob/vs-bijection/notes/vs-bijection.pdf I wasn't sure where stuff like this should go, so I created a |
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Updated with a new commit to include something about homeomorphisms following discussion with @triangle-man. |
Adds some notes about the fact that bijections of vector spaces are also vector spaces, and an example using a stereographic projection of the unit sphere minus the north pole onto the real plane.
Following a discussion with James Geddes, corrects the assertion that there's no bijection between $S^2$ and $\R^2$ and adds in some text about the stereographic projection being a homeomorphism.
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Rebased. Thanks again @rwood-97! |
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Adds some notes about the fact that bijections of vector spaces are also vector spaces.
Explores an example using a stereographic projection of the unit sphere minus the north pole onto the real plane, from @edchapman88's nice question about a vector space that covers the earth.