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

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.

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.

I have a picture for s^3 but how can I see s^3 inside of s^3?
Edit. I meant R3.


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