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  • jxk@sh.itjust.workstoScience Memes@mander.xyzeigenspaces
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    2 months ago

    You want an answer?

    So you’ve probably learned that if u is an eigenvector, then multiplying u by any scalar gives you another eigenvector with the same eigenvalue. That means that the set of all a*u where a is any scalar forms a 1-dimensional space (a line if this is a real vector space). This is an eigenspace of dimension one. The full definition of an eigenspace is as the set of all eigenvectors of a given eigenvalue. Now, if an eigenvalue has multiple independent eigenvectors, then the set of all eigenvectors for that eigenvalue is is still a linear space, but of dimension more than one. So for a real vector space, if an eigenvalue has two sets of independent eigenvectors, its eigenspace will be a 2-dimensional plane.

    That’s pretty much it.












  • Awk has the advantage over Perl/Python/etc. that it’s standardized by POSIX. Therefore you can rely on it on all operating systems. It’s pretty much the only advanced scripting language available that is POSIX – the alternative would be some heavy shell scripting or almost-unreadable sed.