Comments on: Shoulda Series 1: Choosing Bases http://concretenonsense.wordpress.com/2008/04/27/shoulda-series-1-choosing-bases/ A group blog about mathematics Tue, 01 Dec 2009 16:53:01 +0000 http://wordpress.com/ hourly 1 By: Shoulda Series 2: Resolving Ext « Concrete Nonsense http://concretenonsense.wordpress.com/2008/04/27/shoulda-series-1-choosing-bases/#comment-86 Shoulda Series 2: Resolving Ext « Concrete Nonsense Mon, 29 Sep 2008 22:27:37 +0000 http://concretenonsense.wordpress.com/?p=8#comment-86 [...] may or not really count as part of the “Shoulda Series” (1), since I’m pretty sure someone did tell me this at some point. But either way, I had to [...] [...] may or not really count as part of the “Shoulda Series” (1), since I’m pretty sure someone did tell me this at some point. But either way, I had to [...]

]]> By: Pablo Zadunaisky http://concretenonsense.wordpress.com/2008/04/27/shoulda-series-1-choosing-bases/#comment-83 Pablo Zadunaisky Fri, 12 Sep 2008 15:05:21 +0000 http://concretenonsense.wordpress.com/?p=8#comment-83 Your argument seems to be a higher level version of the "basis-free algebra is geometry", that somehow coordinates were introduced to better handle the geometry, but we should be able to introduce the coordinates that better suit every case, and therefore geometric arguments should not depend on what basis we choose. Since Vector Bundles, LCSs, Affine Varieties are somehow geometrical extensions and variations of vector spaces (loosely speaking), an argument about the geometry of spaces independent of basis should be easier to translate into this other cases. Love the idea of the shoulda series! Your argument seems to be a higher level version of the “basis-free algebra is geometry”, that somehow coordinates were introduced to better handle the geometry, but we should be able to introduce the coordinates that better suit every case, and therefore geometric arguments should not depend on what basis we choose. Since Vector Bundles, LCSs, Affine Varieties are somehow geometrical extensions and variations of vector spaces (loosely speaking), an argument about the geometry of spaces independent of basis should be easier to translate into this other cases.

Love the idea of the shoulda series!

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