3 responses to “Linear Independence on a Set of Complex Vectors”

1. 

   Jas, the Physicist

   April 17, 2022 at 3:49 am

   Linear independence in the complex plane doesn’t look the same as the real number line, for obvious reasons. Lines aren’t circles, right? That was basically what all of covering spaces attempted to prove when they created the local homeomorphism of R onto S1. Lines aren’t not circles. Lines locally approximate circles.

   So now, when you think of linear dependence of two vectors in the complex plane, draw me a picture of what you see.

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   1. 

      Jas, the Physicist

      April 20, 2022 at 1:47 pm

      Circles of different periods, or periodically intersecting.

      I know this isn’t a picture. I’ve now moved up to S^n and can’t vizualize as well.

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      1. 

         Jas, the Physicist

         April 20, 2022 at 1:48 pm

         I have a picture for s^3 but how can I see s^3 inside of s^3?

         Edit. I meant R3.

         Reply