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First off, a stupid question: Why does linear indipendance not imply orthogonality? i mean we define the latter such that the inner product is zero i sort of see it as a case of the chicken and the egg, are we using two things to define each other in a cyclical way? Also what extra constraints are placed on orthogonal vectors besides them being linearly independant? I mean if i have two vectors in R2 surely if they are LI they are at right angles? Or am i missing something here...

Also could someone please explain group action with a really simply example as i totally don't get it, and also why you canonly have vector spaces over fields and not rings ( i understand the basic differences between them).

Thanks!

-G

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# Couple of Linear Algebra Questions

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