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Follow up: Show that these vectors are linearly independent almost surely

I posted this question some time ago here. I started a bounty for it and received an answer which helped me a lot. However, I still have some issues I want to discuss regarding it. Unfortunately I can'...
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1 answer
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Show that these vectors are linearly independent almost surely

So I'm doing research in control theory and I have been stuck with this problem for a while. Let me explain my issue, then my proposal, and finally my concrete question. Problem: I have $m<n$ real $...
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